A002767 - OEIS

%I M3820 N1564 #19 Oct 20 2023 10:08:30

%S 5,12,28,54,100,170,284,450,702,1062,1583,2308,3329,4720,6628,9190,

%T 12634,17189,23219,31092,41371,54651,71782,93695,121684,157169,202080,

%U 258579,329509,418096,528518,665521,835170,1044408,1301949,1617830

%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. 26.

%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, 12, 4), x, nmax+1), y, 13), y, 12), x, n), n=0..nmax); # _Sean A. Irvine_, Aug 15 2014

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Aug 15 2014