A350413 Total capacity of unrestricted compositions of n.
0, 0, 0, 0, 1, 6, 24, 79, 233, 640, 1674, 4224, 10370, 24912, 58800, 136767, 314201, 714209, 1608604, 3594007, 7973108, 17576844, 38531060, 84040238, 182467033, 394537387, 849885436, 1824495630, 3904453264, 8331493468, 17730810536, 37641301271, 79727649682, 168512283733
Offset: 1
Keywords
Links
- Aubrey Blecher, Charlotte Brennan, and Arnold Knopfmacher, The water capacity of integer compositions, Online Journal of Analytic Combinatorics, Issue 13, 2018, #6.
Programs
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PARI
v(z, N) = (-2 + 2*N + 5*z - 5*N*z - 4*z^2 + 3*N*z^2)/(-1 + 2*z)^2 + (1 - z)*(-3 + 4*z)/(1 - 2*z)*sum(r=2, N, 1/(1 - 2*z + z^r), O(z*z^N)) + sum(r=2, N, (1 - z)^2/(1 - 2*z + z^r)^2, O(z*z^N)); lista(nn) = Vec(v(z,nn), -nn);