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A305272
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a(n) = 836*2^n - 676.
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4
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160, 996, 2668, 6012, 12700, 26076, 52828, 106332, 213340, 427356, 855388, 1711452, 3423580, 6847836, 13696348, 27393372, 54787420, 109575516, 219151708, 438304092, 876608860, 1753218396, 3506437468, 7012875612, 14025751900, 28051504476, 56103009628, 112206019932, 224412040540, 448824081756
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OFFSET
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0,1
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COMMENTS
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a(n) is the second Zagreb index of the polyphenylene dendrimer G[n], defined pictorially in the Arif et al. reference (see Fig. 1, where G[2] is shown).
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 polyphenylene dendrimer G[n] is M(G[n]; x, y) = (56*2^n - 40)*x^2*y^2 + (48*2^n - 40)*x^2*y^3 +(36* 2^n - 36)*x^3*y^3 + 4*x^3 *y^4.
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LINKS
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FORMULA
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G.f.: 4*(40 + 129*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
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MAPLE
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seq(836*2^n-676, n = 0..40);
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MATHEMATICA
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836*2^Range[0, 40]-676 (* or *) LinearRecurrence[{3, -2}, {160, 996}, 40] (* Harvey P. Dale, Jun 19 2021 *)
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PROG
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(PARI) Vec(4*(40 + 129*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 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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