A328542 Number of 4 dots bracelet partitions of n.

1, 4, 13, 36, 89, 204, 442, 912, 1811, 3480, 6500, 11844, 21117, 36920, 63427, 107244, 178714, 293868, 477321, 766516, 1217968, 1916292, 2987257, 4616520, 7076364, 10763620, 16253303, 24373932, 36312963, 53763672, 79128931, 115802696, 168557574

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..32.

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(4, 64), q, 40));

Crossrefs

Sequence in context: A173723 A002727 A320589 * A036629 A350642 A079922

Adjacent sequences: A328539 A328540 A328541 * A328543 A328544 A328545

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2019

Status

approved