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A051946
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G.f.: (1+4*x)/(1-x)^7.
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4
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1, 11, 56, 196, 546, 1302, 2772, 5412, 9867, 17017, 28028, 44408, 68068, 101388, 147288, 209304, 291669, 399399, 538384, 715484, 938630, 1216930, 1560780, 1981980, 2493855, 3111381, 3851316, 4732336, 5775176, 7002776, 8440432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Kekule numbers for certain benzenoids. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 18 2005
Equals row sums of triangle A143130, & binomial transform of {1, 10, 35, 60, 55, 26, 5, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2008
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p.233, # 5).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n)=C(n+5, 5)*(5n+6)/6.
a(n)=(n+1)(n+2)(n+3)(n+4)(n+5)(5n+6)/720 - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 18 2005
a(n)=A034264(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 14 2008]
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MAPLE
| a:=n->(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(5*n+6)/720: seq(a(n), n=0..35); (Deutsch)
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CROSSREFS
| Partial sums of A027800.
Cf. A093562 ((5, 1) Pascal, column m=6).
Cf. A143130.
Sequence in context: A042503 A079547 A034264 * A201150 A114030 A071984
Adjacent sequences: A051943 A051944 A051945 * A051947 A051948 A051949
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Dec 20 1999
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EXTENSIONS
| Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 18 2005
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