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A000098
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Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3.
(Formerly M1373 N0533)
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10
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1, 2, 5, 10, 19, 33, 57, 92, 147, 227, 345, 512, 752, 1083, 1545, 2174, 3031, 4179, 5719, 7752, 10438, 13946, 18519, 24428, 32051, 41805, 54265, 70079, 90102, 115318, 147005, 186626, 236064, 297492, 373645, 467707
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OFFSET
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0,2
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COMMENTS
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Also number of partitions of 2*n+1 with exactly 3 odd parts (offset 1). - Vladeta Jovovic, Jan 12 2005
Convolution of A000041 and A001399. - Vaclav Kotesovec, Aug 18 2015
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REFERENCES
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H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 90.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
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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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, Transforms
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FORMULA
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Euler transform of 2 2 2 1 1 1 1...
G.f.=1/[(1-x)(1-x^2)(1-x^3)*product((1-x^k), k=1..infinity)].
a(n)=sum(A000097(n-3*j), j=0..floor(n/3)), n>=0.
a(n) ~ sqrt(n) * exp(Pi*sqrt(2*n/3)) / (2*sqrt(2)*Pi^3). - Vaclav Kotesovec, Aug 18 2015
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EXAMPLE
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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'.
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CROSSREFS
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Cf. A000070, A008951, A000097, A000710.
Fourth column of Riordan triangle A008951 and of triangle A103923.
Sequence in context: A018739 A011893 A132210 * A024827 A104161 A065613
Adjacent sequences: A000095 A000096 A000097 * A000099 A000100 A000101
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Edited by Emeric Deutsch, Mar 23 2005
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STATUS
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approved
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