A002768 - OEIS

%I M3831 N1571 #19 Oct 20 2023 10:09:10

%S 5,13,30,59,109,187,312,497,775,1176,1753,2561,3694,5245,7366,10223,

%T 14056,19137,25853,34637,46092,60910,80009,104462,135674,175274

%N Number of bipartite partitions.

%D M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 32.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. S. Cheema and H. Gupta, <a href="/A002755/a002755.pdf">Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956</a>. (Annotated scanned pages from, plus a review)

%p nmax := 20:

%p gf := (n, m, k) -> 1/(product(product(1-x^r*y^t, t=k..m), r=0..n) * product(1-x^s, s=1..n)):

%p seq(coeff(coeff(series(series(gf(nmax, 15, 5), x, nmax+1), y, 16), y, 15), x, n), n=0..nmax); # _Sean A. Irvine_, Aug 15 2014

%K nonn

%O 0,1

%A _N. J. A. Sloane_