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Search: id:A039959
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| A039959 |
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Number of ways of numbering the vertices of a cube so sum of the 8 numbers is n. |
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+0
2
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| 1, 1, 4, 7, 21, 37, 85, 151, 292, 490, 848, 1346, 2157, 3260, 4925, 7148, 10327, 14477, 20177, 27483, 37194, 49431, 65277, 84945, 109873, 140394, 178377, 224334, 280647, 348040, 429526, 526108, 641524, 777127, 937513, 1124461
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. H. Redfield, The theory of group-reduced distributions, Amer. J. Math., 49 (1927), 433-435; reprinted in P. A. MacMahon, Coll. Papers I, pp. 805-827.
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FORMULA
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G.f.: (x^12-x^11+x^10+6*x^8+x^7+8*x^6+x^5+6*x^4+x^2-x+1)/((1-x)(1-x^2)(1-x^3)(1-x^4))^2. - Michael Somos Mar 05 2004
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EXAMPLE
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For n=2 the 4 ways are: {0000 0002}, {0000 0011}, {0001 0100}, {0001 1000}.
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MAPLE
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1/24/(1-x)^8+3/8/(1-x^2)^4+1/3/(1-x^3)^2/(1-x)^2+1/4/(1-x^4)^2;
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PROGRAM
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(PARI) a(n)=if(n<-4, -a(-8-n), polcoeff(subst(Pol([1, -1, -5, 5, 11, -4, -4]), x, x+1/x)*x^6/prod(k=1, 4, 1-x^k)^2+x*O(x^n), n))
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CROSSREFS
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Sequence in context: A066345 A026570 A111955 this_sequence A010363 A119561 A026548
Adjacent sequences: A039956 A039957 A039958 this_sequence A039960 A039961 A039962
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KEYWORD
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nonn
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AUTHOR
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njas
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