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Search: id:A000291
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| A000291 |
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Number of bipartite partitions of n white objects and 2 black ones.
(Formerly M1168 N0447)
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+0
5
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| 2, 4, 9, 16, 29, 47, 77, 118, 181, 267, 392, 560, 797, 1111, 1541, 2106, 2863, 3846, 5142, 6808, 8973, 11733, 15275, 19753, 25443, 32582, 41569, 52770, 66757, 84078, 105555, 131995, 164566, 204450, 253292, 312799, 385285, 473183, 579722, 708353
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of ways to factor p^n*q^2 where p and q are distinct primes.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
Amarnath Murthy, "Generalization of Smarandache Factor Partition introducing Smarandache Factor Partition". Smarandache Notions Journal, 1-2-3, vol. 11, 2000.
Amarnath Murthy, Program for finding out the number of Smarandache Factor Partitions. Smarandache Notions Journal, Vol. 13, 2002.
Amarnath Murthy, e-book, MS LIT format, "Ideas on Smarandache Notions".
Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 1.9, 1.14.
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EXAMPLE
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a(2) = 9: let p = 2 and q = 3, p^2*q^2 = 36; there are 9 factorizations: (36), (18*2), (12*3), (9*4), (9*2^2), (6*6), (6*3*2), (4*3^2), (3^2*2^2).
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CROSSREFS
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Column 2 of A060243. Cf. A005380.
Sequence in context: A023194 A114080 A090676 this_sequence A081055 A034446 A034452
Adjacent sequences: A000288 A000289 A000290 this_sequence A000292 A000293 A000294
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004
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