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Search: id:A001978
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| A001978 |
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Number of partitions of 3n-1 into n nonnegative integers each no more than 6.
(Formerly M2725 N1092)
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+0
1
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| 1, 3, 8, 16, 32, 55, 94, 147, 227, 332, 480, 668, 920, 1232, 1635, 2124, 2738, 3470, 4368, 5424, 6695, 8172, 9922, 11934, 14287, 16968, 20068, 23572, 27584, 32087, 37199, 42901, 49325, 56450, 64424, 73223, 83012, 93764, 105661, 118674, 133003
(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 3n-1 involving the letters a, b, c, d, e, f, g, having weights 0, 1, 2, 3, 4, 5, 6 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)), where w=3n-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)); n=400; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(d=1, 60, w=3*d-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. A001977.
Sequence in context: A068039 A081661 A005103 this_sequence A077552 A024623 A027291
Adjacent sequences: A001975 A001976 A001977 this_sequence A001979 A001980 A001981
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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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