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Search: id:A107915
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| A107915 |
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(1/75)binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4). |
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+0
4
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| 1, 35, 490, 4116, 24696, 116424, 457380, 1557270, 4723719, 13026013, 33157124, 78835120, 176729280, 376375104, 766192176, 1498581756, 2828205765, 5168991135, 9177226366, 15870391460, 26794167400, 44253495000, 71627692500
(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.
Partial sums of A107917. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 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. 229).
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FORMULA
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a(n)=C(n,n-2)*C(n+1,n-3)*C(n+2,n-4)/(5*3!), n>=4 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2007
a(n-3) = 1/144*sum {1 <= x_1, x_2, x_3 <= n} x_1*x_2*x_3*(det V(x_1,x_2,x_3))^2 = 1/144*sum {1 <= i,j,k <= n} i*j*k*((i-j)(i-k)(j-k))^2, where V(x_1,x_2,x_3) is the Vandermonde matrix of order 3. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
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MAPLE
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a:=n->(1/75)*binomial(n+4, 4)*binomial(n+5, 4)*binomial(n+6, 4): seq(a(n), n=0..27);
seq(binomial(n, n-2)*binomial(n+1, n-3)*binomial(n+2, n-4)/(5*3!), n=4..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2007
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CROSSREFS
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Cf. A047819, A107917, A133708.
Sequence in context: A075664 A133317 A105947 this_sequence A114342 A010951 A033281
Adjacent sequences: A107912 A107913 A107914 this_sequence A107916 A107917 A107918
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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 12 2005
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