Search: id:A000291
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%I A000291 M1168 N0447
%S A000291 2,4,9,16,29,47,77,118,181,267,392,560,797,1111,1541,2106,2863,3846,
%T A000291 5142,6808,8973,11733,15275,19753,25443,32582,41569,52770,66757,84078,
%U A000291 105555,131995,164566,204450,253292,312799,385285,473183,579722,708353
%N A000291 Number of bipartite partitions of n white objects and 2 black ones.
%C A000291 Number of ways to factor p^n*q^2 where p and q are distinct primes.
%D A000291 F. C. Auluck, On partitions of bipartite numbers. Proc. Cambridge Philos. 
               Soc. 49, (1953). 72-83.
%D A000291 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.
%D A000291 Amarnath Murthy, "Generalization of Smarandache Factor Partition introducing 
               Smarandache Factor Partition". Smarandache Notions Journal, 1-2-3, 
               vol. 11, 2000.
%D A000291 Amarnath Murthy, Program for finding out the number of Smarandache Factor 
               Partitions. Smarandache Notions Journal, Vol. 13, 2002.
%D A000291 Amarnath Murthy, e-book, MS LIT format, "Ideas on Smarandache Notions".
%D A000291 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.
%D A000291 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000291 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%e A000291 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).
%Y A000291 Column 2 of A060243. Cf. A005380.
%Y A000291 Sequence in context: A023194 A114080 A090676 this_sequence A081055 A034446 
               A034452
%Y A000291 Adjacent sequences: A000288 A000289 A000290 this_sequence A000292 A000293 
               A000294
%K A000291 nonn
%O A000291 0,1
%A A000291 N. J. A. Sloane (njas(AT)research.att.com).
%E A000291 Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004

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