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A001976
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Number of partitions of floor(5n/2)-1 into n nonnegative integers each no more than 5.
(Formerly M2545 N1006)
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1
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0, 1, 3, 6, 11, 19, 32, 48, 71, 101, 141, 188, 249, 322, 414, 518, 645, 791, 966, 1160, 1389, 1645, 1943, 2268, 2642, 3053, 3521, 4026, 4596, 5214, 5907, 6648, 7473, 8359, 9339, 10380, 11526, 12747, 14085, 15498, 17039, 18671, 20444, 22308, 24326, 26452, 28746
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OFFSET
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0,3
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COMMENTS
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In Cayley's terminology, this is the number of literal terms of degree n and of weight floor(5n/2)-1 involving the letters a, b, c, d, e, f, having weights 0, 1, 2, 3, 4, 5 respectively. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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REFERENCES
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A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281.
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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Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 1, -2, 2, -2, 2, -2, 0, 2, -2, 2, -2, 2, -1, 0, 1, -2, 1).
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FORMULA
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Coefficient of x^w*z^n in the expansion of 1/((1-z)(1-xz)(1-x^2z)(1-x^3z)(1-x^4z)(1-x^5z)), where w=floor(5n/2)-1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
G.f.: -(x^12 +x^11 +x^10 +2*x^9 +2*x^8 +4*x^7 +x^6 +4*x^5 +2*x^4 +2*x^3 +x^2 +x+1)*x / ((x^4+1) *(x^2+x+1) *(x^2-x+1) *(x^2+1)^2 *(x+1)^3 *(x-1)^5). - Alois P. Heinz, Jul 25 2015
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PROG
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(PARI) f=1/((1-z)*(1-x*z)*(1-x^2*z)*(1-x^3*z)*(1-x^4*z)*(1-x^5*z)); n=350; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(d=0, 60, w=floor(5*d/2)-1; print1(polcoeff(polcoeff(p, w), d)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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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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Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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STATUS
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approved
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