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Search: id:A001980
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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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+0
1
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, p. 276-281.
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LINKS
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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, p. 276-281.
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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
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PROGRAM
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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=1, 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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Cf. A001979.
Sequence in context: A008268 A084446 A158671 this_sequence A057750 A118645 A137531
Adjacent sequences: A001977 A001978 A001979 this_sequence A001981 A001982 A001983
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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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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