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A108674
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(n+1)^2*(n+2)^2*(2*n+3)/12.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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
| 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
| Sequence in context: A102360 A060581 A065103 * A050405 A206383 A020136
Adjacent sequences: A108671 A108672 A108673 * A108675 A108676 A108677
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 17 2005
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