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

1,6

Links

Table of n, a(n) for n=1..34.

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

Cf. A201126, A285766.

Sequence in context: A359133 A011855 A173031 * A361474 A004404 A319552

Adjacent sequences: A350410 A350411 A350412 * A350414 A350415 A350416

Keyword

nonn

Author

Michel Marcus, Dec 29 2021

Status

approved