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%I #4 Oct 19 2019 12:10:22
%S 1,3,8,19,41,83,161,298,535,934,1591,2653,4344,6992,11088,17346,26799,
%T 40933,61871,92607,137366,202044,294833,427054,614273,877758,1246479,
%U 1759674,2470278,3449412,4792265,6625706,9118302,12493167,17044656
%N Number of broken 3-diamond partitions of n.
%D Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI: broken diamonds and modular forms. Acta Arith. 126, 281-294 (2007)
%D 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.
%F 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) ).
%p Q := (a,q,M) -> mul(1-a*q^r, r=0..M-1);
%p Deltak := (k,M) -> Q(-q,q,M)/( Q(q,q,M)^2 * Q(-q^(2*k+1),q^(2*k+1),M) );
%p seriestolist(series(Deltak(3,64),q,40));
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 19 2019
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