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A002765 Number of bipartite partitions.
(Formerly M4495 N1902)
0

%I M4495 N1902 #20 Oct 20 2023 10:06:49

%S 8,23,57,119,231,415,719,1189,1915,2997,4595,6898,10198,14833,21303,

%T 30211,42393,58869,81028,110551,149683,201160,268539,356167,469630,

%U 615712,803029,1042051,1345896,1730473,2215561,2825037,3588364,4541036

%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. 11.

%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 := 35:

%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, 9, 2), x, nmax+1), y, 10), y, 9), x, n), n=0..nmax); # _Sean A. Irvine_, Aug 14 2014

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Aug 14 2014

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Last modified April 16 11:08 EDT 2024. Contains 371711 sequences. (Running on oeis4.)