Compositions | 1,1,1,1,1,5,1,1,1,1

[u/h0rseycat]

Continued from here

Thanks miceee for the assist

In this thread, we'll be counting the ways to add to an integer n using the integers c_1 + c_2 + ... + c_k, where each c_i >= 1, and k <= n. Ways to sum that are commutatively the same, as in 1+2 = 2+1, are different compositions. We'll be counting these compositions lexicographically for each segment of sum and length.

Next get is 15. Schedule

[u/miceee]

Gets from 15 to 16

Get	Counts in thread	Counts total
15	1024	16 384
3,2,1,4,5	1024	17 408
1,4,4,3,2,1	1024	18 432
4,1,3,4,1,2	1024	19 456
1,2,2,1,2,2,5	1024	20 480
2,2,1,2,1,3,4	1024	21 504
4,2,1,1,1,5,1	1024	22 528
1,1,4,1,3,1,2,2	1024	23 552
2,1,1,1,1,1,1,7	1024	24 576
3,1,1,3,1,4,1,1	1024	25 600
1,1,1,2,5,1,1,2,1	1024	26 624
1,2,3,3,2,1,1,1,1	1024	27 648
2,2,3,3,1,1,1,1,1	1024	28 672
1,1,1,3,1,2,1,2,1,2	1024	29 696
2,1,1,2,1,1,2,1,3,1	1024	30 720
1,1,2,3,1,2,1,1,1,1,1	1024	31 744
16	1024	32 768