A328540 - OEIS

%I #4 Oct 19 2019 12:09:53

%S 1,3,8,19,41,82,158,291,519,901,1527,2533,4128,6615,10445,16273,25044,

%T 38108,57393,85606,126553,185533,269886,389719,558900,796317,1127628,

%U 1587498,2222571,3095346,4289282,5915331,8120558,11099168,15106787

%N Number of broken 2-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(2,64),q,40));

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 19 2019