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A350413
Total capacity of unrestricted compositions of n.
0
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
1,6
LINKS
Aubrey Blecher, Charlotte Brennan, and Arnold Knopfmacher, The water capacity of integer compositions, Online Journal of Analytic Combinatorics, Issue 13, 2018, #6.
PROG
(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);
CROSSREFS
Sequence in context: A359133 A011855 A173031 * A361474 A004404 A319552
KEYWORD
nonn
AUTHOR
Michel Marcus, Dec 29 2021
STATUS
approved