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A277976
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a(n) = n*(3*n + 23).
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1
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0, 26, 58, 96, 140, 190, 246, 308, 376, 450, 530, 616, 708, 806, 910, 1020, 1136, 1258, 1386, 1520, 1660, 1806, 1958, 2116, 2280, 2450, 2626, 2808, 2996, 3190, 3390, 3596, 3808, 4026, 4250, 4480, 4716, 4958, 5206, 5460, 5720, 5986, 6258, 6536
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OFFSET
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0,2
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COMMENTS
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For n >= 3, a(n) is the second Zagreb index of the graph obtained by joining one vertex of the cycle graph C[n] with each vertex of a second cycle graph C[n].
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
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LINKS
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FORMULA
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G.f.: 2*x*(13-10*x)/(1-x)^3.
Sum_{n>=1} 1/a(n) = 823467/5539688 + sqrt(3)*Pi/138-3*log(3)/46 = 0.11643041... - R. J. Mathar, Apr 22 2024
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EXAMPLE
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a(4) = 140. Indeed, the corresponding graph has 12 edges. We list the degrees of their endpoints: (2,2), (2,2), (2,6), (2,6), (3,3), (3,3), (3,3), (3,3), (3,6), (3,6), (3,6), (3,6). Then, the second Zagreb index is 4 + 4 + 12 + 12 + 9 + 9 + 9 + 9 + 18 + 18 + 18 + 18 = 140.
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MAPLE
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seq(n*(3*n+23), n = 0..50);
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MATHEMATICA
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Table[n(3n+23), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 26, 58}, 50] (* Harvey P. Dale, Sep 30 2017 *)
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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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