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A328539 Number of broken 1-diamond partitions of n. 0
1, 3, 8, 18, 38, 75, 142, 258, 455, 780, 1308, 2148, 3467, 5505, 8618, 13314, 20327, 30693, 45882, 67944, 99745, 145239, 209882, 301128, 429148, 607710, 855414, 1197228, 1666585, 2308014, 3180668, 4362762, 5957444, 8100192, 10968478, 14793954 (list; graph; refs; listen; history; text; internal format)
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..35.

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(1, 64), q, 40));

CROSSREFS

Sequence in context: A000713 A261325 A261446 * A078409 A036642 A000235

Adjacent sequences:  A328536 A328537 A328538 * A328540 A328541 A328542

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 19 2019

STATUS

approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)