Consider Pascal’s triangle given below. Cover the odd numbers with small black discs (or shade the numbers). What do you notice about the pattern obtained?

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 1 11 55 165 330 462 462 330 165 55 11 1 1 12 66 220 495 792 924 792 495 220 66 12 1 1 13 78 286 715 x0 x1 x1 x0 715 286 78 13 1 1 14 91 364 x2 x3 x4 x5 x4 x3 x2 364 91 14 1 1 15 105 455 x6 x7 x8 x9 x9 x8 x7 x6 455 105 15 1 where x0 = 1287, x1 = 1716, x2 = 1001, x3 = 2002, x4 = 3003, x5 = 3432, x6 = 1365, x7 = 3003, x8 = 5005, and x9 = 6435.