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Search: id:A107891
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| A107891 |
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(1/2880)(n+1)(n+2)^2*(n+3)^2*(n+4)(3n^2+15n+20). |
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+0
7
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| 1, 19, 155, 805, 3136, 9996, 27468, 67320, 150645, 313027, 611611, 1134497, 2012920, 3436720, 5673648, 9093096, 14194881, 21643755, 32310355, 47319349, 68105576, 96479020, 134699500, 185562000, 252493605, 339663051, 452103939
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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 A114239. First differences of A047819. - 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 (see pp. 167, 187, and p. 105 eq. (iii) for k=2 and m=5).
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FORMULA
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a(n-2) = 1/8*sum {1 <= x_1, x_2 <= n} (x_1*x_2)^2*(det V(x_1,x_2))^2 = 1/8*sum {1 <= i,j <= n} (i*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->(1/2880)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(3*n^2+15*n+20): seq(a(n), n=0..32);
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CROSSREFS
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Cf. A005585, A006542, A047819, A114239, A114242.
Sequence in context: A126514 A010825 A022711 this_sequence A141923 A142128 A038864
Adjacent sequences: A107888 A107889 A107890 this_sequence A107892 A107893 A107894
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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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