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Search: id:A114242
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| A114242 |
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a(n)=(n+1)(n+2)^2*(n+3)^2*(n+4)(2n+5)/720. |
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+0
7
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| 1, 14, 90, 385, 1274, 3528, 8568, 18810, 38115, 72358, 130130, 223587, 369460, 590240, 915552, 1383732, 2043621, 2956590, 4198810, 5863781, 8065134, 10939720, 14651000, 19392750, 25393095, 32918886, 42280434, 53836615, 68000360
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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 A114244. First differences of A006857. - 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 (pp. 167-169, Table 10.5/II/2 and p. 105, eq. (ii) K(Ob(2,4,n))).
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FORMULA
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G.f.=(1+x)(1+5x+x^2)/(1-x)^8.
a(n-2) = 1/6*sum {1 <= x_1, x_2 <= n} (x_1)^2*x_2*(det V(x_1,x_2))^2 = 1/6*sum {1 <= i,j <= n} i^2*j*(i-j)^2, where V(x_1,x_2} is the Vandermonde matrix of order 2. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
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MAPLE
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a:=n->(n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n+5)/720: seq(a(n), n=0..30);
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CROSSREFS
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Cf. A005585, A006542, A107891.
Sequence in context: A116343 A034544 A077538 this_sequence A054487 A047639 A010930
Adjacent sequences: A114239 A114240 A114241 this_sequence A114243 A114244 A114245
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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), Nov 18 2005
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