A328543 Number of 5 dots bracelet partitions of n.

1, 5, 19, 60, 169, 435, 1050, 2400, 5250, 11060, 22562, 44740, 86539, 163695, 303500, 552560, 989460, 1745025, 3034670, 5209240, 8834663, 14815240, 24583588, 40390560, 65745538, 106079820, 169741260, 269475500, 424621150, 664344055

Offset

0,2

References

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..29.

Formula

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

Maple

Q := (a, q, M) -> mul(1-a*q^r, r=0..M-1);
BBBk := (k, M) -> Q(-q, q, M)/( Q(q, q, M)^(k-1) * Q(-q^k, q^k, M) );
seriestolist(series(BBBk(5, 64), q, 40));

Crossrefs

Sequence in context: A332720 A092442 A341711 * A135266 A124123 A189714

Adjacent sequences: A328540 A328541 A328542 * A328544 A328545 A328546

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2019

Status

approved