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A277984
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a(n) = 6*n*(9*n-5).
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1
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0, 24, 156, 396, 744, 1200, 1764, 2436, 3216, 4104, 5100, 6204, 7416, 8736, 10164, 11700, 13344, 15096, 16956, 18924, 21000, 23184, 25476, 27876, 30384, 33000, 35724, 38556, 41496, 44544, 47700, 50964, 54336, 57816, 61404, 65100, 68904, 72816, 76836, 80964, 85200
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OFFSET
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0,2
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COMMENTS
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For n>=1, a(n) is the first Zagreb index of the circumcoronene B[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. The definition of the circumcoronene can be viewed in the Gutman et al. and in the Farahani et al. references.
The M-polynomial of the circumcoronene B[n] is M(B[n],x,y) = 6*x^2*y^2 + 12*(n-1)*x^2*y^3 + 3*(3*n-2)*(n-1)*x^3*y^3.
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LINKS
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FORMULA
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G.f.: 12*x*(2+7*x)/(1-x)^3.
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MAPLE
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seq(54*n^2-30*n, n = 0 .. 40);
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MATHEMATICA
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CoefficientList[Series[12 x (2 + 7 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Nov 13 2016 *)
LinearRecurrence[{3, -3, 1}, {0, 24, 156}, 50] (* Harvey P. Dale, Apr 10 2022 *)
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PROG
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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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