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Search: id:A001977
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| A001977 |
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Number of partitions of 3n into n parts from the set {0, 1,.., 6} (repetitions admissible).
(Formerly M3335 N1342)
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+0
3
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| 1, 1, 4, 8, 18, 32, 58, 94, 151, 227, 338, 480, 676, 920, 1242, 1636, 2137, 2739, 3486, 4370, 5444, 6698, 8196, 9926, 11963, 14293, 17002, 20076, 23612, 27594, 32134, 37212, 42955, 49341, 56512, 64444, 73294, 83036, 93844, 105690, 118765, 133037
(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 weight 3*n involving the letters a, b, c, d, e, f, g, having weights 0, 1, 2, 3, 4, 5, 6 respectively, a number which is also equal to the coefficient of x^(3n)z^n in the development of 1/((1-z)(1-xz)(1-x^2z)(1-x^3z)(1-x^4z)(1-x^5z)(1-x^6z)). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 16 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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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=200; p=subst(subst(f, x, x+x*O(x^n)), z, z+z*O(z^n)); for(n=0, 60, print1(polcoeff(polcoeff(p, 3*n), n)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 16 2008
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CROSSREFS
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Adjacent sequences: A001974 A001975 A001976 this_sequence A001978 A001979 A001980
Sequence in context: A077474 A009918 A008085 this_sequence A008373 A008374 A008240
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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 16 2008
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