Enrollment forecasting is a critically important task for colleges and universities. Having a reliable forecast of future enrollment is needed to predict tuition and other
Enrollment forecasting is a critically important task for colleges and universities. Having a reliable forecast of future enrollment is needed to predict tuition and other revenue as well as faculty and staffing needs, course and section offerings, student services, etc.
There are many different facets to enrollment which need to be understood to best plan particular aspects of a universitys operations. For example, to properly plan course offerings, one must be able to predict the number of students in different majors and those students class standing. On the other hand, revenue predictions and student services planning rely on more aggregate enrollment information.
This case study focuses on forecasting aggregate enrollment at California University of Pennsylvania for Fall 2021. The provided data set includes 8 time series:
- GRF2FHC = graduate student, face to face, head count (i.e. the number of students enrolled and registered in face-to-face/on campus graduate programs)
- GRF2FCR = graduate student, face to face, credits (i.e. the number of credits registered by face-to-face/on campus graduate students)
- GROLHC = graduate student, online, head count
- GROLCR = graduate student, online, credits
- UGF2FHC = undergraduate student, face to face, head count (i.e. the number of students enrolled and registered in face-to-face/on campus undergraduate programs)
- UGF2FCR = undergraduate student, face to face, credits (i.e. the number of credits registered by face-to-face/on campus undergraduate students)
- UGOLHC = undergraduate student, online, head count
- UGOLCR = undergraduate student, online, credits
Weekly data has been provided for the 19 weeks leading up to the start of the Fall 2018, 2019 and 2020 terms (APW_19, APW_18, etc.), along with the values on the first day of classes (APRSOT), the next two weeks (APW+01 and APW+02), and the census date (APRCEN, which is 3 weeks into the term, and is the official enrollment number for each semester). Some data for Fall 2021 is also available. An Excel spreadsheet with the data has been provided.
For this case you are to develop a forecast for the remaining weeks to the census date for Fall 2021 for each of the 8 time series. (Note that the census date prediction is the important value; however, having intermediate forecasts can help decision makers understand whether enrollment is falling below or above the prediction).
You are to present your forecast in a professional memo to the Vice President for Enrollment Management. The memo should be written in as non-technical terms as possible and should, in addition to providing the census date forecasts, also attempt to provide insight into what the forecasts mean. (For example, are there discernable trends or changes in enrollment that need to be planned for?). In addition to the memo, you should provide a technical appendix that explains, in detail, the process followed in creating your forecasts (how was the data manipulated, what models were attempted, how were they evaluated, how and why was the final model chosen). Appropriate data visualizations should be provided.
Home Insert Draw Page Layout Formulas Data Review View Tell me X Calibri (Body) 12 V = AA ab Wrap Text General ILI DI Dv Paste v a. Av V Merge & Center $ - % -28 Conditional Format Formatting as Table G85 x Bold J B D N TERM APW_16 A 1 YEAR 2 2018 3 2018 4 2018 5 2018 6 2018 7 2018 8 2018 9 2018 10 2018 11 2018 12 2018 13 2018 14 2018 15 2018 16 2018 17 2018 18 2018 19 2018 20 2018 21 2018 22 2018 23 2018 24 2018 25 2019 26 2019 27 2019 28 2019 29 2019 30 2019 31 2019 32 2019 33 2019 34 2019 35 3019 Fall 2018 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201930 201930 201930 201930 201930 201930 201930 201930 201930 201930 501930 Sheet1 TERMNAME FREEZE Fall 2018 APW_19 Fall 2018 APW_18 Fall 2018 APW_17 Fall 2018 Fall 2018 Fall 2018 ADW 15 Fall 2018 APW_15 Fall 2018 AW APW_14 2010 Aow 12 Fall 2018 APW_13 Fall 2018 APW_12 El 2010 Aow Fall 2018 APW_11 El 2010 AW 10 Fall 2018 APW_10 El 2040 nown Fall 2018 APW_09 now ng Fall 2018 APW_08 El 2010 Fall 2018 APW_07 El 2040 Fall 2018 APW_06 Fall 2018 APW_05 Fall 2010 Fall 2018 APW_04 APW APW_03 Fall 2018 APW_02 Fall 2018 APW_01 Fall 2018 APRSOT Fall 2018 Fall 2010 APW+01 Fall 2018 APW+02 Fall 2018 APRCEN 10 Fall 2019 1 APW_19 Fall 2019 APW_18 Fan 2015 - Fall 2019 APW_17 Ann- Fall 2019 1 APW_16 wo Fall 2019 1 APW_15 Fall 2019 2012 APW_14 Fall 2019 1 APW_13 Fall 2019 APW_12 Fall 2019 APW_11 Fall 2019 APW_10 Fall 2019 APM 09 + E F G H 1 J K L M FREEZEDATE GRF2FHC GRF2FCR GRGOLHC GRGOLCR UGF2FHC UGF2FCR UGGOLHC UGGOLCR 4/16/2018 3:00 AM 234 2058.5 347 2304 2328 31869 332 3194 4/23/2018 3:00 AM 254 2209 448 2997 2692 37133 380 3669 4/30/2018 3:00 AM 267 2306 547 2627 3627 3004 41600 442 4231 442 4231 5/7/2018 3:00 AM 07 297 5/7/2018 3:00 AM 2540.5 635 109 4224 3114 43201 492 4686 5/14/2018 3:00 AM 312 28575 2657.5 co 694 2570 on 4578 1584 3262 E 45461 539 5204 5/21/2018 2:00 AM 25 325 2708 5/21/2018 3:00 AM En 2786.5 27 757 5007 2926 3336 AREZ EOE 46679 585 5639 12010010 AM 290 339 5/28/2018 3:00 AM 2940.5 704 5944 5241 AEC 3456 18500 COE 794 48589 5220 605 5830 6/4/2018 3:00 AM 353 DER 2080 220 3069.5 5500 20 5508 ene 40200 co 838 3504 49298 628 6086 6/11/2018 3:00 AM 384 2900 2 3336.5 570 882 5796 3563 CA 5014 50145 647 6317 6/18/2018 3:00 AM 20 MBA 040 con 2640 5009 399 6021 918 6697 50943 3619 669 6527 B125/2010 2.00AM 445 ro 6409 3595 947 285 6/25/2018 3:00 AM 6192 704 415 cone 54574 3665 51571 704 6906 27012018 2:00 AM 2044 24 00 434 BAMA 3814 983 700 2808 7/2/2018 3:00 AM 6444 Fon 3696 ZE 52083 759 7304 10/2016 2 AM AEG 100 2074 458 2200 BREA 7 1020 7/9/2018 3:00 AM 3974 6654 59247 3709 52347 7500 782 7508 7/16/2018 3:00 AM 463 4082 1050 8010 aze 1059 3781 6918 7095 53477 827 7925 7/23/2018 3:00 AM 470 47 4450 4150.5 1089 7086 2824 EZER 3821 2207 866 54154 8307 7/30/2018 3:00 AM 477 4292.5 1134 040 7377 3852 54700 2770 54728 919 8778 8/6/2018 3:00 AM non 1407 4341.5 por 2870 480 1197 7785 3879 061 55085 184 961 9164 8/13/2018 3:00 AM 527 AREZ 4667 1816 1316 8469 3926 56069 1030 9801 8/20/2018 3:00 AM 622 5148 1404 8964 3978 56896 1081 10368 8/27/2018 3:00 AM 666 5330 1458 9303 3998 57038 1146 11081 10. w 9/3/2018 3:00 AM 676 5327 1478 9426 4024 57483 1182 11398 9/10/2018 3:00 AM 672 1472 5300 Wow ! 9381 4016 57452 1177 11318 9/18/2018 3:00 AM w 668 5273 1470 4002 072010 9354 ware 1172 57173 11264 4/15/2019 3:00 AM 200 186 1544 297 1914 2061 28076 138 1239 4/22/2019 8:11 AM 209 1739 367 2355 2478 34362 198 1795 www. ** 4/29/2019 3:00 AM 226 1881.5 409 2583 2818 39100 278 WWW. 2573 5/6/2019 3:00 AM wome 252 2049.5 481 3018 41692 3003 357 .. wo 3277 5/13/2019 3:00 AM 281 2278 548 3411 WWW ! 3153 44102 432 4057 5/20/2019 3:00 AM 304 2470 585 3660 3228 45291 507 4689 5/27/2019 3:00 AM 323 2732 617 3858 3321 46735 544 5062 . were 6/3/2019 3:00 AM 336 2889 639 4020 3397 47867 589 5454 6/10/2019 3:00 AM 351 3030 687 4320 3432 48516 622 5811 6/17/2019 3:00 AM 360 3108 761 4782 3469 48920 635 5971 6/24/2019 3:00 AM 285 2227 R14 5154 3517 4978A 656 6155 Dondu D E F G H K L M B 34 2019 201930 35 2019 201930 36 2019 201930 37 2019 201930 38 2019 201930 39 2019 201930 40 2019 201930 41 2019 201930 42 2019 201930 43 2019 201930 44 2019 201930 45 2019 201930 46 2019 201930 47 2019 201930 48 2020 202030 49 2020 202030 50 2020 202030 51 2020 202030 52 2020 202030 53 2020 202030 54 2020 202030 55 2020 202030 56 2020 202030 57 2020 202030 58 2020 202030 59 2020 202030 60 2020 202030 61 2020 202030 62 2020 202030 63 2020 202030 64 2020 202030 65 2020 202030 66 2020 202030 67 2020 202030 68 2020 202030 69 2020 202030 70 2020 202030 71 2021 202130 72 2021 202130 73 2021 202130 74 2021 202130 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2021 Fall 2021 Fall 2021 Fall 2021 APW_10 APW_09 APW_08 APW_07 APW_06 APW_05 APW_04 APW_03 APW_02 APW_01 APRSOT APW+01 APW+02 APRCEN APW_19 APW_18 APW_17 APW_16 APW_15 APW_14 APW_13 APW_12 APW_11 APW_10 APW_09 APW_08 APW_07 APW_06 APW_05 APW_04 APW_03 APW_02 APW_01 APRSOT APW+01 APW+02 APRCEN APW_19 APW_18 APW_17 APW_16 6/17/2019 3:00 AM 6/24/2019 3:00 AM 7/1/2019 3:00 AM 7/8/2019 3:00 AM 7/15/2019 3:00 AM 7/22/2019 3:00 AM 7/29/2019 3:00 AM 8/5/2019 3:00 AM 8/12/2019 3:00 AM 8/19/2019 3:00 AM 8/26/2019 3:00 AM 9/2/2019 3:00 AM 9/9/2019 3:00 AM 9/17/2019 7:52 AM 4/13/2020 3:00 AM 4/20/2020 3:00 AM 4/27/2020 3:00 AM 5/4/2020 3:00 AM 5/11/2020 3:00 AM 5/18/2020 3:00 AM 5/25/2020 3:00 AM 6/1/2020 3:00 AM 6/8/2020 3:00 AM 6/15/2020 3:00 AM 6/22/2020 3:00 AM 6/29/2020 3:00 AM 7/6/2020 3:00 AM 7/13/2020 3:00 AM 7/20/2020 3:00 AM 7/27/2020 3:00 AM 8/3/2020 3:00 AM 8/10/2020 3:00 AM 8/17/2020 3:00 AM 8/24/2020 3:00 AM 8/31/2020 3:00 AM 9/7/2020 3:00 AM 9/15/2020 3:00 AM 4/12/2021 3:00 AM 4/19/2021 3:00 AM 4/26/2021 3:00 AM 5/3/2021 3:00 AM 360 385 400 408 417 428 433 445 461 478 550 573 568 566 165 181 220 232 253 268 286 295 310 341 362 371 386 395 406 419 437 468 480 522 536 534 533 257 272 302 318 3108 3327 3433 3532 3733 3863 3919 4080 4345 4510 4770 4764 4725 4706 1337 1486 1789 2014 2196 2340 2484 2583 2718 3049 3236 3315 3472 3556 3679 3759 3989 4200 4260 4473 4548 4533 4518 2309 2462 2742 2895 761 814 860 899 968 1036 1086 1145 1240 1322 1425 1441 1434 1420 349 469 548 629 682 723 756 791 857 932 1054 1121 1170 1224 1306 1382 1434 1484 1545 1593 1585 1576 1567 636 694 727 780 4782 5154 5403 5643 6039 6496.5 6849 7218 7809 8364 9060 9129 9072 8985 2178 2874 3360 3855 4194 4485 4704 4956 5310 5835 6609 7047 7386 7779 8301 8760 9114 9451 9793 10097 9980 9902 9821 3993 4314 4539 4860 3469 3517 3573 3583 3626 3686 3704 3727 3781 3848 3850 3863 3858 3834 2072 2680 2916 3063 3162 3211 3311 3353 3397 3431 3480 3525 3549 3572 3608 3645 3690 3683 3700 3695 3745 3730 3721 2215 2516 2652 2753 48920 49786 50605 50682 51310 52200 52469 52856 53615 54648 54591 54841 54864 54473 28350 36880 40530 42716 44069 44709 46202 46829 47454 48006 48542 49273 49637 50058 50734 51246 51869 51621 51927 51683 52432 52240 52007 30294 34209 35878 37188 635 656 703 729 771 800 813 852 885 969 1015 1046 1040 1022 277 408 468 509 558 594 653 689 714 735 748 774 797 828 853 886 930 965 1018 1056 1082 1069 1064 5971 6155 6676 6994 7390 7702 7826 8238 8506 9317 9738 9888 9800 9604 2655 3903 4426 4779 5219 5596 6051 6376 6628 6807 6974 7206 7429 7716 7976 8349 8820 9136 9712 10099 10322 10177 10103 4449 4839 5278 5506 474 513 556 582 Home Insert Draw Page Layout Formulas Data Review View Tell me X Calibri (Body) 12 V = AA ab Wrap Text General ILI DI Dv Paste v a. Av V Merge & Center $ - % -28 Conditional Format Formatting as Table G85 x Bold J B D N TERM APW_16 A 1 YEAR 2 2018 3 2018 4 2018 5 2018 6 2018 7 2018 8 2018 9 2018 10 2018 11 2018 12 2018 13 2018 14 2018 15 2018 16 2018 17 2018 18 2018 19 2018 20 2018 21 2018 22 2018 23 2018 24 2018 25 2019 26 2019 27 2019 28 2019 29 2019 30 2019 31 2019 32 2019 33 2019 34 2019 35 3019 Fall 2018 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201830 201930 201930 201930 201930 201930 201930 201930 201930 201930 201930 501930 Sheet1 TERMNAME FREEZE Fall 2018 APW_19 Fall 2018 APW_18 Fall 2018 APW_17 Fall 2018 Fall 2018 Fall 2018 ADW 15 Fall 2018 APW_15 Fall 2018 AW APW_14 2010 Aow 12 Fall 2018 APW_13 Fall 2018 APW_12 El 2010 Aow Fall 2018 APW_11 El 2010 AW 10 Fall 2018 APW_10 El 2040 nown Fall 2018 APW_09 now ng Fall 2018 APW_08 El 2010 Fall 2018 APW_07 El 2040 Fall 2018 APW_06 Fall 2018 APW_05 Fall 2010 Fall 2018 APW_04 APW APW_03 Fall 2018 APW_02 Fall 2018 APW_01 Fall 2018 APRSOT Fall 2018 Fall 2010 APW+01 Fall 2018 APW+02 Fall 2018 APRCEN 10 Fall 2019 1 APW_19 Fall 2019 APW_18 Fan 2015 - Fall 2019 APW_17 Ann- Fall 2019 1 APW_16 wo Fall 2019 1 APW_15 Fall 2019 2012 APW_14 Fall 2019 1 APW_13 Fall 2019 APW_12 Fall 2019 APW_11 Fall 2019 APW_10 Fall 2019 APM 09 + E F G H 1 J K L M FREEZEDATE GRF2FHC GRF2FCR GRGOLHC GRGOLCR UGF2FHC UGF2FCR UGGOLHC UGGOLCR 4/16/2018 3:00 AM 234 2058.5 347 2304 2328 31869 332 3194 4/23/2018 3:00 AM 254 2209 448 2997 2692 37133 380 3669 4/30/2018 3:00 AM 267 2306 547 2627 3627 3004 41600 442 4231 442 4231 5/7/2018 3:00 AM 07 297 5/7/2018 3:00 AM 2540.5 635 109 4224 3114 43201 492 4686 5/14/2018 3:00 AM 312 28575 2657.5 co 694 2570 on 4578 1584 3262 E 45461 539 5204 5/21/2018 2:00 AM 25 325 2708 5/21/2018 3:00 AM En 2786.5 27 757 5007 2926 3336 AREZ EOE 46679 585 5639 12010010 AM 290 339 5/28/2018 3:00 AM 2940.5 704 5944 5241 AEC 3456 18500 COE 794 48589 5220 605 5830 6/4/2018 3:00 AM 353 DER 2080 220 3069.5 5500 20 5508 ene 40200 co 838 3504 49298 628 6086 6/11/2018 3:00 AM 384 2900 2 3336.5 570 882 5796 3563 CA 5014 50145 647 6317 6/18/2018 3:00 AM 20 MBA 040 con 2640 5009 399 6021 918 6697 50943 3619 669 6527 B125/2010 2.00AM 445 ro 6409 3595 947 285 6/25/2018 3:00 AM 6192 704 415 cone 54574 3665 51571 704 6906 27012018 2:00 AM 2044 24 00 434 BAMA 3814 983 700 2808 7/2/2018 3:00 AM 6444 Fon 3696 ZE 52083 759 7304 10/2016 2 AM AEG 100 2074 458 2200 BREA 7 1020 7/9/2018 3:00 AM 3974 6654 59247 3709 52347 7500 782 7508 7/16/2018 3:00 AM 463 4082 1050 8010 aze 1059 3781 6918 7095 53477 827 7925 7/23/2018 3:00 AM 470 47 4450 4150.5 1089 7086 2824 EZER 3821 2207 866 54154 8307 7/30/2018 3:00 AM 477 4292.5 1134 040 7377 3852 54700 2770 54728 919 8778 8/6/2018 3:00 AM non 1407 4341.5 por 2870 480 1197 7785 3879 061 55085 184 961 9164 8/13/2018 3:00 AM 527 AREZ 4667 1816 1316 8469 3926 56069 1030 9801 8/20/2018 3:00 AM 622 5148 1404 8964 3978 56896 1081 10368 8/27/2018 3:00 AM 666 5330 1458 9303 3998 57038 1146 11081 10. w 9/3/2018 3:00 AM 676 5327 1478 9426 4024 57483 1182 11398 9/10/2018 3:00 AM 672 1472 5300 Wow ! 9381 4016 57452 1177 11318 9/18/2018 3:00 AM w 668 5273 1470 4002 072010 9354 ware 1172 57173 11264 4/15/2019 3:00 AM 200 186 1544 297 1914 2061 28076 138 1239 4/22/2019 8:11 AM 209 1739 367 2355 2478 34362 198 1795 www. ** 4/29/2019 3:00 AM 226 1881.5 409 2583 2818 39100 278 WWW. 2573 5/6/2019 3:00 AM wome 252 2049.5 481 3018 41692 3003 357 .. wo 3277 5/13/2019 3:00 AM 281 2278 548 3411 WWW ! 3153 44102 432 4057 5/20/2019 3:00 AM 304 2470 585 3660 3228 45291 507 4689 5/27/2019 3:00 AM 323 2732 617 3858 3321 46735 544 5062 . were 6/3/2019 3:00 AM 336 2889 639 4020 3397 47867 589 5454 6/10/2019 3:00 AM 351 3030 687 4320 3432 48516 622 5811 6/17/2019 3:00 AM 360 3108 761 4782 3469 48920 635 5971 6/24/2019 3:00 AM 285 2227 R14 5154 3517 4978A 656 6155 Dondu D E F G H K L M B 34 2019 201930 35 2019 201930 36 2019 201930 37 2019 201930 38 2019 201930 39 2019 201930 40 2019 201930 41 2019 201930 42 2019 201930 43 2019 201930 44 2019 201930 45 2019 201930 46 2019 201930 47 2019 201930 48 2020 202030 49 2020 202030 50 2020 202030 51 2020 202030 52 2020 202030 53 2020 202030 54 2020 202030 55 2020 202030 56 2020 202030 57 2020 202030 58 2020 202030 59 2020 202030 60 2020 202030 61 2020 202030 62 2020 202030 63 2020 202030 64 2020 202030 65 2020 202030 66 2020 202030 67 2020 202030 68 2020 202030 69 2020 202030 70 2020 202030 71 2021 202130 72 2021 202130 73 2021 202130 74 2021 202130 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2019 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2020 Fall 2021 Fall 2021 Fall 2021 Fall 2021 APW_10 APW_09 APW_08 APW_07 APW_06 APW_05 APW_04 APW_03 APW_02 APW_01 APRSOT APW+01 APW+02 APRCEN APW_19 APW_18 APW_17 APW_16 APW_15 APW_14 APW_13 APW_12 APW_11 APW_10 APW_09 APW_08 APW_07 APW_06 APW_05 APW_04 APW_03 APW_02 APW_01 APRSOT APW+01 APW+02 APRCEN APW_19 APW_18 APW_17 APW_16 6/17/2019 3:00 AM 6/24/2019 3:00 AM 7/1/2019 3:00 AM 7/8/2019 3:00 AM 7/15/2019 3:00 AM 7/22/2019 3:00 AM 7/29/2019 3:00 AM 8/5/2019 3:00 AM 8/12/2019 3:00 AM 8/19/2019 3:00 AM 8/26/2019 3:00 AM 9/2/2019 3:00 AM 9/9/2019 3:00 AM 9/17/2019 7:52 AM 4/13/2020 3:00 AM 4/20/2020 3:00 AM 4/27/2020 3:00 AM 5/4/2020 3:00 AM 5/11/2020 3:00 AM 5/18/2020 3:00 AM 5/25/2020 3:00 AM 6/1/2020 3:00 AM 6/8/2020 3:00 AM 6/15/2020 3:00 AM 6/22/2020 3:00 AM 6/29/2020 3:00 AM 7/6/2020 3:00 AM 7/13/2020 3:00 AM 7/20/2020 3:00 AM 7/27/2020 3:00 AM 8/3/2020 3:00 AM 8/10/2020 3:00 AM 8/17/2020 3:00 AM 8/24/2020 3:00 AM 8/31/2020 3:00 AM 9/7/2020 3:00 AM 9/15/2020 3:00 AM 4/12/2021 3:00 AM 4/19/2021 3:00 AM 4/26/2021 3:00 AM 5/3/2021 3:00 AM 360 385 400 408 417 428 433 445 461 478 550 573 568 566 165 181 220 232 253 268 286 295 310 341 362 371 386 395 406 419 437 468 480 522 536 534 533 257 272 302 318 3108 3327 3433 3532 3733 3863 3919 4080 4345 4510 4770 4764 4725 4706 1337 1486 1789 2014 2196 2340 2484 2583 2718 3049 3236 3315 3472 3556 3679 3759 3989 4200 4260 4473 4548 4533 4518 2309 2462 2742 2895 761 814 860 899 968 1036 1086 1145 1240 1322 1425 1441 1434 1420 349 469 548 629 682 723 756 791 857 932 1054 1121 1170 1224 1306 1382 1434 1484 1545 1593 1585 1576 1567 636 694 727 780 4782 5154 5403 5643 6039 6496.5 6849 7218 7809 8364 9060 9129 9072 8985 2178 2874 3360 3855 4194 4485 4704 4956 5310 5835 6609 7047 7386 7779 8301 8760 9114 9451 9793 10097 9980 9902 9821 3993 4314 4539 4860 3469 3517 3573 3583 3626 3686 3704 3727 3781 3848 3850 3863 3858 3834 2072 2680 2916 3063 3162 3211 3311 3353 3397 3431 3480 3525 3549 3572 3608 3645 3690 3683 3700 3695 3745 3730 3721 2215 2516 2652 2753 48920 49786 50605 50682 51310 52200 52469 52856 53615 54648 54591 54841 54864 54473 28350 36880 40530 42716 44069 44709 46202 46829 47454 48006 48542 49273 49637 50058 50734 51246 51869 51621 51927 51683 52432 52240 52007 30294 34209 35878 37188 635 656 703 729 771 800 813 852 885 969 1015 1046 1040 1022 277 408 468 509 558 594 653 689 714 735 748 774 797 828 853 886 930 965 1018 1056 1082 1069 1064 5971 6155 6676 6994 7390 7702 7826 8238 8506 9317 9738 9888 9800 9604 2655 3903 4426 4779 5219 5596 6051 6376 6628 6807 6974 7206 7429 7716 7976 8349 8820 9136 9712 10099 10322 10177 10103 4449 4839 5278 5506 474 513 556 582
