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Search: id:A001975
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| A001975 |
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Number of partitions of floor(5n/2) into n nonnegative integers each no more than 5.
(Formerly M2551 N1010)
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+0
4
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| 1, 1, 3, 6, 12, 20, 32, 49, 73, 102, 141, 190, 252, 325, 414, 521, 649, 795, 967, 1165, 1394, 1651, 1944, 2275, 2649, 3061, 3523, 4035, 4604, 5225, 5910, 6660, 7483, 8372, 9343, 10395, 11538, 12764, 14090, 15516, 17053, 18691, 20451, 22330, 24342, 26476
(list; graph; listen)
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OFFSET
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0,3
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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(5n/2) 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, 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)), where w=floor(5n/2). - 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)); 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); print1(polcoeff(polcoeff(p, w), d)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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CROSSREFS
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Sequence in context: A125851 A066140 A061061 this_sequence A096220 A034333 A006128
Adjacent sequences: A001972 A001973 A001974 this_sequence A001976 A001977 A001978
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KEYWORD
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nonn
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AUTHOR
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njas
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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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