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A069983
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Number of 5-gonal compositions of n into positive parts.
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2
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0, 0, 0, 0, 0, 1, 5, 15, 35, 65, 121, 185, 305, 420, 640, 826, 1190, 1470, 2030, 2430, 3246, 3795, 4935, 5665, 7205, 8151, 10175, 11375, 13975, 15470, 18746, 20580, 24640, 26860, 31820, 34476, 40460, 43605, 50745, 54435, 62871, 67165
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OFFSET
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0,7
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 17.
G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, Europ. J. Combin., 22 (2001), 887-904.
Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).
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FORMULA
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G.f.: q^5/(1-q)^5 - 5*q^9/((1-q)^5*(1+q)^4).
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n > 9. - Colin Barker, Sep 18 2019
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MATHEMATICA
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Table[Piecewise[{
{Binomial[k - 1, k - 5] - 5*Binomial[(k - 1)/2, (k - 9)/2], Mod[k, 2] == 1},
{Binomial[k - 1, k - 5] - 5*Binomial[(k - 2)/2, (k - 10)/2], Mod[k, 2] == 0}
}], {k, 1, 20}] (* Mo Li, Sep 18 2019 *)
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PROG
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(PARI) concat([0, 0, 0, 0, 0], Vec(x^5*(1 + 4*x + 6*x^2 + 4*x^3 - 4*x^4) / ((1 - x)^5*(1 + x)^4) + O(x^40))) \\ Colin Barker, Sep 18 2019
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CROSSREFS
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Cf. A069981, A069982, A005044.
Sequence in context: A233348 A061829 A063382 * A005894 A015622 A341134
Adjacent sequences: A069980 A069981 A069982 * A069984 A069985 A069986
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 06 2002
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STATUS
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approved
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