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A328542 Number of 4 dots bracelet partitions of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A079922 A053563

Adjacent sequences:  A328539 A328540 A328541 * A328543 A328544 A328545

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 19 2019

STATUS

approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)