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A000412
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Number of bipartite partitions of n white objects and 3 black ones.
(Formerly M2657 N1060)
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3
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3, 7, 16, 31, 57, 97, 162, 257, 401, 608, 907, 1325, 1914, 2719, 3824, 5313, 7316, 9973, 13495, 18105, 24132, 31938, 42021, 54948, 71484, 92492, 119120, 152686, 194887, 247693, 313613, 395547, 497154, 622688, 777424, 967525, 1200572
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Number of ways to factor p^n*q^3 where p and q are distinct primes.
a(n) = if n <= 3 then A054225(3,n) else A054225(n,3). [Reinhard Zumkeller, Nov 30 2011]
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REFERENCES
| F. C. Auluck, On partitions of bipartite numbers. Proc. Cambridge Philos. Soc. 49, (1953). 72-83.
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. 1.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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CROSSREFS
| Column 3 of A054225.
Cf. A005380.
Sequence in context: A117491 A110585 A184677 * A192964 A179904 A161810
Adjacent sequences: A000409 A000410 A000411 * A000413 A000414 A000415
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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