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Search: id:A034263
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| 1, 9, 39, 119, 294, 630, 1218, 2178, 3663, 5863, 9009, 13377, 19292, 27132, 37332, 50388, 66861, 87381, 112651, 143451, 180642, 225170, 278070, 340470, 413595, 498771, 597429, 711109, 841464, 990264, 1159400, 1350888, 1566873
(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. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2005
5-dimensional form of hexagonal-based pyramid numbers. - Ben Creech (mathroxmysox(AT)yahoo.com), Nov 17 2005
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pps. 1-8.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 167-169, Table 10.5/II/4).
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FORMULA
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G.f.: (1+3*x)/(1-x)^6.
a(n) = n*(n+1)*(n+2)*(n+3)*(4*n+1)/120. - Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ben Creech (mathroxmysox(AT)yahoo.com), Nov 17 2005
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MAPLE
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a:=n->(n+1)*(n+2)*(n+3)*(n+4)*(4*n+5)/120: seq(a(n), n=0..35); (Deutsch)
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CROSSREFS
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Partial sums of A002417. Also a(n)=f(n+1, 3) where f is given in A034261.
a(n)= A093561(n+5, 5), (4, 1)-Pascal column.
Sequence in context: A023163 A054121 A139594 this_sequence A060929 A124851 A124041
Adjacent sequences: A034260 A034261 A034262 this_sequence A034264 A034265 A034266
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu); Barry E. Williams, Dec 13 1999
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EXTENSIONS
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Corrected and extended Apr 21 2000 - njas
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