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A304375
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a(n) = 27*n^2/2 + 45*n/2 - 12 (n>=1).
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2
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24, 87, 177, 294, 438, 609, 807, 1032, 1284, 1563, 1869, 2202, 2562, 2949, 3363, 3804, 4272, 4767, 5289, 5838, 6414, 7017, 7647, 8304, 8988, 9699, 10437, 11202, 11994, 12813, 13659, 14532, 15432, 16359, 17313, 18294, 19302, 20337, 21399, 22488, 23604, 24747, 25917, 27114, 28338, 29589, 30867, 32172, 33504
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OFFSET
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1,1
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COMMENTS
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a(n) is the second Zagreb index of the triangular benzenoid T(n) (see the M. Ghorbani et al. references).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of the triangular benzenoid T(n) is M(T(n); x,y) = 6*x^2*y^2 + 6*(n-1)*x^2*y^3 + 3*n*(n-1)*x^3*y^3/2.
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LINKS
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FORMULA
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G.f.: 3*x*(8 + 5*x - 4*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
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MAPLE
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seq(27*n^2/2 + 45*n/2 - 12, n=1..50);
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MATHEMATICA
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Table[(27n^2)/2+(45n)/2-12, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {24, 87, 177}, 50] (* Harvey P. Dale, Dec 30 2023 *)
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PROG
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(PARI) a(n) = 27*n^2/2 + 45*n/2 - 12; \\ Altug Alkan, May 12 2018
(PARI) Vec(3*x*(8 + 5*x - 4*x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 12 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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