A226541 Number of unimodal compositions of n where the maximal part appears three times.

1, 0, 0, 1, 0, 0, 1, 2, 3, 5, 7, 11, 16, 24, 34, 51, 71, 102, 143, 201, 276, 384, 522, 714, 964, 1301, 1739, 2328, 3084, 4085, 5377, 7064, 9226, 12036, 15616, 20228, 26092, 33584, 43067, 55125, 70308, 89502, 113598, 143889, 181755, 229160, 288186, 361750, 453046, 566346, 706464

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

G.f.: sum(n>=0, x^(3*n) / prod(k=1..n-1, 1-x^k )^2 ); replace 3 by m to obtain g.f. for "... max part appears m times".

a(n) ~ Pi^2 * exp(2*Pi*sqrt(n/3)) / (16 * 3^(7/4) * n^(9/4)). - Vaclav Kotesovec, Oct 24 2018

Prog

(PARI) N=66; x='x+O('x^N); Vec(sum(n=0, N, x^(3*n) / prod(k=1, n-1, 1-x^k )^2 ))

Crossrefs

Cf. A006330 (max part appears once), A114921 (max part appears twice).

Cf. A188674 (max part m appears m times), A001522 (max part m appears at least m times).

Cf. A001523 (max part appears any number of times).

Cf. A000009 (symmetric, max part m appears once; also symmetric, max part appears an odd number of times).

Cf. A035363 (symmetric, max part m appears twice; also symmetric, max part appears an even number of times).

Cf. A087897 (symmetric, max part m appears 3 times).

Cf. A027349 (symmetric, max part m appears m times), A189357 (symmetric, max part m appears at least m times).

Column k=3 of A247255.

Sequence in context: A308991 A326467 A326592 * A281578 A173199 A023435

Adjacent sequences: A226538 A226539 A226540 * A226542 A226543 A226544

Keyword

nonn

Author

Joerg Arndt, Jun 10 2013

Status

approved