A328541 - OEIS

%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