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Search: id:A008795
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| A008795 |
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Molien series for 3-dimensional group [2,n]+ = 22n. |
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+0
4
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| 1, 0, 3, 1, 6, 3, 10, 6, 15, 10, 21, 15, 28, 21, 36, 28, 45, 36, 55, 45, 66, 55, 78, 66, 91, 78, 105, 91, 120, 105, 136, 120, 153, 136, 171, 153, 190, 171, 210, 190, 231, 210, 253, 231, 276, 253, 300, 276, 325, 300
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n-3) = number of ordered triples of positive integers which are the side lengths of a nondegenerate triangle of perimeter n. - Rob Pratt (Rob.Pratt(AT)sas.com), Jul 12 2004
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REFERENCES
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Ira Rosenholtz, Problem 1584, Mathematics Magazine, Vol. 72 (1999), p. 408.
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LINKS
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Index entries for Molien series
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FORMULA
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The signed version with g.f. (1-x^3)/(1-x^2)^3 is the inverse binomial transform of A084861. - Paul Barry (pbarry(AT)wit.ie), Jun 12 2003
a(n) = binom(n/2+2, 2) for n even, binom((n+1)/2, 2) for n odd - Rob Pratt (Rob.Pratt(AT)sas.com), Jul 12 2004
a(n-2) interleaves n(n+1)/2 and n(n-1)/2. G.f.: (1-x+x^2)/((1+x)^2(1-x)^3)); a(n)=(2n^2+6n+7)/16+3(2n+3)(-1)^n/16. - Paul Barry (pbarry(AT)wit.ie), Jul 29 2004
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MAPLE
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(1+x^3)/(1-x^2)^3
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MATHEMATICA
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Table[If[EvenQ[n], Binomial[n/2+2, 2], Binomial[(n+1)/2, 2]], {n, 0, 49}]
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CROSSREFS
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Cf. A005044.
First differences of A053307.
Sequence in context: A107884 A158822 A121443 this_sequence A165188 A132180 A126191
Adjacent sequences: A008792 A008793 A008794 this_sequence A008796 A008797 A008798
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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