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A003292
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Number of 4-line partitions of n decreasing across rows.
(Formerly M1050)
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2
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1, 2, 4, 7, 11, 19, 29, 46, 70, 106, 156, 232, 334, 482, 686, 971, 1357, 1894, 2612, 3592, 4900, 6656, 8980, 12077, 16137, 21490, 28476, 37600, 49422, 64763, 84511, 109953, 142539, 184244, 237368, 304996, 390688, 499189, 636059, 808489, 1025017, 1296595, 1636173, 2060246, 2588440, 3245381, 4060519, 5070574
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of unlabeled graphs on n nodes whose connected components are a path or a cycle. - Geoffrey Critzer, Nov 28 2011
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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).
Herbert S. Wilf, Generatingfunctiontology, Academic Press, 1994, page 106.
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LINKS
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FORMULA
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G.f.: Product (1 - x^k)^-{c(k)}; c(k) = 1, 1, 2, 2, 2, 2, ....
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MATHEMATICA
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Rest[p=Product[1/(1 - x^i), {i, 1, 20}]; CoefficientList[Series[p^2 (1 - x) (1 - x^2), {x, 0, 20}], x]] (* Geoffrey Critzer, Nov 28 2011 *) (* adapted by Vincenzo Librandi, Oct 12 2017 *)
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PROG
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(PARI) \\ program includes a(0) = 1:
c(n) = 1 + (n>=3);
N = 66; x = 'x + O('x^N);
Vec( 1 / prod(n=1, N, (1 - x^k)^c(n)) ) \\ Joerg Arndt, Oct 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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