Search: id:A000098
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%I A000098 M1373 N0533
%S A000098 1,2,5,10,19,33,57,92,147,227,345,512,752,1083,1545,2174,3031,4179,5719,
%T A000098 7752,10438,13946,18519,24428,32051,41805,54265,70079,90102,115318,
%U A000098 147005,186626,236064,297492,373645,467707
%N A000098 Number of partitions of n if there are two kinds of 1, two kinds of 2 
               and two kinds of 3.
%C A000098 Also number of partitions of 2*n+1 with exactly 3 odd parts (offset 1). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2005
%D A000098 H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, 
               Vol. 4, Cambridge Univ. Press, 1958, p. 90.
%D A000098 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
%D A000098 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000098 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000098 T. D. Noe, <a href="b000098.txt">Table of n, a(n) for n=0..1000</a>
%H A000098 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A000098 Euler transform of 2 2 2 1 1 1 1...
%F A000098 G.f.=1/[(1-x)(1-x^2)(1-x^3)*product((1-x^k), k=1..infinity)].
%F A000098 a(n)=sum(A000097(n-3*j), j=0..floor(n/3)), n>=0.
%e A000098 a(3)=10 because we have 3, 3', 2+1, 2+1', 2'+1, 2'+1', 1+1+1, 1+1+1', 
               1+1'+1' and 1'+1'+1'.
%Y A000098 Cf. A000070, A008951, A000097, A000710.
%Y A000098 Fourth column of Riordan triangle A008951 and of triangle A103923.
%Y A000098 Sequence in context: A018739 A011893 A132210 this_sequence A024827 A104161 
               A065613
%Y A000098 Adjacent sequences: A000095 A000096 A000097 this_sequence A000099 A000100 
               A000101
%K A000098 nonn,easy
%O A000098 0,2
%A A000098 N. J. A. Sloane (njas(AT)research.att.com).
%E A000098 Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005

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