Backgiound, Fibonacci Sequence You probably have all seen, or at least heard about, the Fibonacci sequence, named after Italian mathematician Leonardo of Pisa, known as Fibonacci. It is a sequence based on a starting set of numbers and a way to calculate subsequent numbers The starting sequence for the Fibonacci numbers requires two seed numbers, typically 1 and 1 (though there is some variation if you look at the web page https://en.wikipedia.org/wiki/Fibonacci number). All subsequent numbers are based on the sum of the two (which is important for our purposes, see below) previous numbers. It is often written as a recurrence relation: Fn-Fn-1 + Fn-2 Thus the Fibonacci sequence is 1,1, 2, 3, 5, 8, 13, 21, 34. 55, 89, 14-4 Where the seed numbers required to start the sequence are marked in bold. That is, the seed numbers are required to be present before the calculations can begin Fibonacci n-step sequences But why should we restrict ourselves to 2-seeds and the sum of the 2-previous numbers. Why not 3, 6, 9 etc? Sure, why not. We can generalize to Fibonacci n-step numbers where n represents both the number of seeds required and the number of previous values that are added to create the next number in the sequence. Here are some examples fibonacci tribonacci tetranacoI 112358 13 21 34 55 89 144 233 377 610 1124713 24 44 81 149 274 504 927 1705 3136 1 124815 29 56 108 208 401 773 1490 2872 5536 entanacci 11 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 hexanacci heptanacci 1124 8 16 32 64 127 253 504 1004 2000 3984 7936 octonacCI nonanacCI decanacci 1 1 248 16 32 63 125 248 492 976 1936 3840 7617 1 1248 16 32 64 128 255 509 1016 2028 4048 8080 1 1248 16 32 64 128 256 511 1021 2040 4076 8144 1 1248 16 32 64 128 256 512 1023 2045 4088 8172 10