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Search: id:A108674
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| A108674 |
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(n+1)^2*(n+2)^2*(2*n+3)/12. |
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+0
2
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| 1, 15, 84, 300, 825, 1911, 3920, 7344, 12825, 21175, 33396, 50700, 74529, 106575, 148800, 203456, 273105, 360639, 469300, 602700, 764841, 960135, 1193424, 1470000, 1795625, 2176551, 2619540, 3131884, 3721425, 4396575, 5166336
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Kekule numbers for certain benzenoids.
This is the case P(3,n) of the family of sequences defined in A132458. - Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p.231, # 33).
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FORMULA
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G.f.=(1+z)(1+8z+z^2)/(1-z)^6
Also a(n) = Sum[Sum[i*j^2, {i, 1, n+1}], {j, 1, n+1}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 25 2006
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MAPLE
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a:=n->(n+1)^2*(n+2)^2*(2*n+3)/12: seq(a(n), n=0..35);
a:=n->sum(k^2*sum(k, k=0..n), k=0..n):seq(a(n), n=1...31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 01 2008
a:=n->sum(k^2*sum(k, k=0..n), k=0..n):seq(a(n), n=1...31); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 09 2008]
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CROSSREFS
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Sequence in context: A102360 A060581 A065103 this_sequence A050405 A020136 A067401
Adjacent sequences: A108671 A108672 A108673 this_sequence A108675 A108676 A108677
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 17 2005
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