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A049612
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a(n) = T(n,3), array T as in A049600.
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10
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0, 1, 5, 19, 63, 192, 552, 1520, 4048, 10496, 26624, 66304, 162560, 393216, 940032, 2224128, 5214208, 12124160, 27983872, 64159744, 146210816, 331350016, 747110400, 1676673024, 3746562048, 8338276352, 18488492032
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OFFSET
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0,3
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COMMENTS
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If X_1, X_2, ..., X_n are 2-blocks of a (2n+3)-set X then, for n >= 1, a(n+1) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007
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REFERENCES
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Robert Cori, Gabor Hetyei, Genus one partitions, in 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AT, pp. 333-344, <hal-01207612>
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LINKS
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R. Cori and G. Hetyei, How to count genus one partitions, FPSAC 2014, Chicago, Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France, 2014, 333-344.
S. Kitaev and J. Remmel, p-Ascent Sequences, arXiv preprint arXiv:1503.00914 [math.CO], 2015.
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FORMULA
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G.f.: x*(1-x)^3 /(1-2*x)^4.
a(n) = Sum_{k=0..floor((n+3)/2)} C(n+3, 2k)*C(k+1, 3). - Paul Barry, May 15 2003
a(n+1) = 2^n*n^3/48 + 5*2^n*n^2/16 + 7*2^n*n/6 + 2^n, n>=1. - Milan Janjic, Nov 18 2007
Binomial transform of the tetrahedral numbers A000292 when omitting the initial 0 in both sequences. - Carl Najafi, Sep 08 2011
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MATHEMATICA
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CoefficientList[Series[x (1-x)^3/(1-2x)^4, {x, 0, 30}], x] (* or *) Join[ {0}, LinearRecurrence[{8, -24, 32, -16}, {1, 5, 19, 63}, 30]] (* Harvey P. Dale, Jan 07 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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