A328540 Number of broken 2-diamond partitions of n.

1, 3, 8, 19, 41, 82, 158, 291, 519, 901, 1527, 2533, 4128, 6615, 10445, 16273, 25044, 38108, 57393, 85606, 126553, 185533, 269886, 389719, 558900, 796317, 1127628, 1587498, 2222571, 3095346, 4289282, 5915331, 8120558, 11099168, 15106787

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(2, 64), q, 40));

Crossrefs

Sequence in context: A007326 A136396 A006380 * A260547 A328541 A182818

Adjacent sequences: A328537 A328538 A328539 * A328541 A328542 A328543

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2019

Status

approved