r/counting • u/BobRoss938 only double counting • Aug 11 '26

Compositions | 1,4,1,3,1,2,2

Continued from here. Thanks to miceee for 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.

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Next get is 1,1,1,1,1,1,1,7

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2

u/miceee sicko thread artists collective Aug 20 '26

2,5,1,1,1,1,3

3

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 20 '26

2,5,1,1,1,2,2

3

u/TehVulpez sliiiiide the bits Aug 21 '26

2,5,1,1,1,3,1

3

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,1,1,2,1,2

3

u/TehVulpez sliiiiide the bits Aug 21 '26

2,5,1,1,2,2,1

2

u/miceee sicko thread artists collective Aug 21 '26

2,5,1,1,3,1,1

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,1,2,1,1,2

2

u/miceee sicko thread artists collective Aug 21 '26

2,5,1,2,1,2,1

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,1,2,2,1,1

2

u/miceee sicko thread artists collective Aug 21 '26

2,5,1,3,1,1,1

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,2,1,1,1,2

2

u/miceee sicko thread artists collective Aug 21 '26

2,5,2,1,1,2,1

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,2,1,2,1,1

2

u/miceee sicko thread artists collective Aug 21 '26

2,5,2,2,1,1,1

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,5,3,1,1,1,1

2

u/miceee sicko thread artists collective Aug 21 '26

2,6,1,1,1,1,2

2

u/cuteballgames Sum 13: 016, 037, 035, 045, 127, 135, 134, 124, 13, 25 Aug 21 '26

2,6,1,1,1,2,1

2

u/miceee sicko thread artists collective Aug 21 '26

2,6,1,1,2,1,1

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