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A001980
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Number of partitions of floor(7n/2)-1 into n nonnegative integers each no greater than 7.
(Formerly M3388 N1368)
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2
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0, 1, 4, 10, 23, 48, 94, 166, 285, 464, 734, 1109, 1646, 2371, 3366, 4652, 6357, 8519, 11309, 14754, 19103, 24399, 30956, 38797, 48355, 59665, 73264, 89145, 108011, 129864, 155554, 185017, 219336, 258438, 303604, 354665, 413213, 479048, 554033
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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(7n/2)-1 involving the letters a, b, c, d, e, f, g, h, having weights 0, 1, 2, 3, 4, 5, 6, 7 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 (1, 1, -1, 2, -1, -2, 0, -1, 0, 1, 2, 2, -1, -2, 1, -4, 0, 4, -1, 2, 1, -2, -2, -1, 0, 1, 0, 2, 1, -2, 1, -1, -1, 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)(1-x^6z)(1-x^7z)), where w=floor(7n/2)-1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
G.f.: -(x^24 +3*x^23 +5*x^22 +10*x^21 +17*x^20 +26*x^19 +33*x^18 +45*x^17 +55*x^16 +61*x^15 +63*x^14 +68*x^13 +67*x^12 +68*x^11 +63*x^10 +61*x^9 +55*x^8 +45*x^7 +33*x^6 +26*x^5 +17*x^4 +10*x^3 +5*x^2 +3*x +1)*x / ((x^4+x^3+x^2+x+1) *(x^4-x^2+1) *(x^2+x+1)^2 *(x^2-x +1)^2 *(x^2+1)^3 *(x+1)^5 *(x-1)^7). - 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)*(1-x^6*z)*(1-x^7*z)); n=400; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(d=0, 60, w=floor(7*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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