A328541 Number of broken 3-diamond partitions of n.

1, 3, 8, 19, 41, 83, 161, 298, 535, 934, 1591, 2653, 4344, 6992, 11088, 17346, 26799, 40933, 61871, 92607, 137366, 202044, 294833, 427054, 614273, 877758, 1246479, 1759674, 2470278, 3449412, 4792265, 6625706, 9118302, 12493167, 17044656

Offset

0,2

References

Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI: broken diamonds and modular forms. Acta Arith. 126, 281-294 (2007)

Cui, Su-Ping, and Nancy SS Gu. "Congruences for broken 3-diamond and 7 dots bracelet partitions." The Ramanujan Journal 35.1 (2014): 165-178.

Links

Table of n, a(n) for n=0..34.

Formula

We write (a;q)_M as Q(a,q,M). The g.f. for the number of broken k-diamond partitions of n is Q(-q,q,oo)/( Q(q,q,oo)^2 * Q(-q^(2*k+1),q^(2*k+1),oo) ).

Maple

Q := (a, q, M) -> mul(1-a*q^r, r=0..M-1);
Deltak := (k, M) -> Q(-q, q, M)/( Q(q, q, M)^2 * Q(-q^(2*k+1), q^(2*k+1), M) );
seriestolist(series(Deltak(3, 64), q, 40));

Crossrefs

Sequence in context: A006380 A328540 A260547 * A182818 A095846 A153732

Adjacent sequences: A328538 A328539 A328540 * A328542 A328543 A328544

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2019

Status

approved