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A328542
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Number of 4 dots bracelet partitions of n.
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0
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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
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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FORMULA
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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) ).
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MAPLE
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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));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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