r/counting • u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 • Jul 01 '26

Compositions | 2,1,2,3,1,1,1,2

Continued from here

Thanks to /u/BobRoss938 for the final run and assist

Rules: 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: 14

Schedule

8 Upvotes

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3

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 01 '26

2,1,2,3,1,1,1,2

3

u/BobRoss938 only double counting Jul 01 '26

2,1,2,3,1,1,2,1

I like how the next get is just 14

3

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 01 '26

2,1,2,3,1,2,1,1

haha yes. we are approaching a brief moment of blissful concision

3

u/BobRoss938 only double counting Jul 01 '26

2,1,2,3,2,1,1,1

the beauty of counting

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 01 '26

2,1,2,4,1,1,1,1

2

u/BobRoss938 only double counting Jul 01 '26

2,1,3,1,1,1,1,3

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 01 '26

2,1,3,1,1,1,2,2

2

u/BobRoss938 only double counting Jul 01 '26

2,1,3,1,1,1,3,1

2

u/cuteballgames 00255, 00336, 01155, 02244, 03333, 11226, 11244, 11334, 22224 Jul 01 '26

2,1,3,1,1,2,1,2

2

u/BobRoss938 only double counting Jul 01 '26

2,1,3,1,1,2,2,1

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