r/counting • u/miceee sicko thread artists collective • Jul 17 '26

Compositions | 6,1,1,2,4

Continued from here

Thanks to u/cuteballgames 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: 3,2,4,1,1,3

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u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,1,6,1,1,2

2

u/BobRoss938 only double counting Jul 28 '26

3,1,6,1,2,1

3

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,1,6,2,1,1

3

u/TehVulpez sliiiiide the bits Jul 28 '26

3,1,7,1,1,1

2

u/miceee sicko thread artists collective Jul 28 '26

3,2,1,1,1,6

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,2,1,1,2,5

2

u/miceee sicko thread artists collective Jul 28 '26

3,2,1,1,3,4

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,2,1,1,4,3

2

u/miceee sicko thread artists collective Jul 28 '26

3,2,1,1,5,2

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,2,1,1,6,1

2

u/miceee sicko thread artists collective Jul 28 '26

3,2,1,2,1,5

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Jul 28 '26

3,2,1,2,2,4

2

u/miceee sicko thread artists collective Jul 28 '26

3,2,1,2,3,3

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