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A305075
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a(n) = 32*n - 24 (n>=1).
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2
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8, 40, 72, 104, 136, 168, 200, 232, 264, 296, 328, 360, 392, 424, 456, 488, 520, 552, 584, 616, 648, 680, 712, 744, 776, 808, 840, 872, 904, 936, 968, 1000, 1032, 1064, 1096, 1128, 1160, 1192, 1224, 1256, 1288, 1320, 1352, 1384, 1416, 1448, 1480, 1512, 1544, 1576
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OFFSET
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1,1
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COMMENTS
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a(n) (n>=2) is the second Zagreb index of the single oxide chain SOX(n), defined pictorially in the Simonraj et al. reference (Fig. 4, where SOX(9) is shown marked as OX(1,9)).
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 SL(n) is M(SL(n);x,y) = 2*x^2*y^2 + 2*n*x^2*y^4 + (n - 2)*x^4*y^4 (n>=2).
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LINKS
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FORMULA
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G.f.: 8*x*(1 + 3*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)
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MAPLE
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seq(32*n - 24, n = 1 .. 50);
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MATHEMATICA
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32*Range[60]-24 (* or *) LinearRecurrence[{2, -1}, {8, 40}, 60] (* Harvey P. Dale, Mar 13 2022 *)
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PROG
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(PARI) Vec(8*x*(1 + 3*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 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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