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A278128
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a(n) = 288*2^n - 156.
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1
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132, 420, 996, 2148, 4452, 9060, 18276, 36708, 73572, 147300, 294756, 589668, 1179492, 2359140, 4718436, 9437028, 18874212, 37748580, 75497316, 150994788, 301989732, 603979620, 1207959396, 2415918948, 4831838052, 9663676260, 19327352676, 38654705508
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OFFSET
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0,1
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COMMENTS
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a(n) is the first Zagreb index of the phenylazomethine dendrimer G[n], defined pictorially in the Golriz et al. reference (Fig. 1). 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 M-polynomial of the dendrimer G[n] is M(G[n],x,y) = (24*2^n - 8)*x^2*y^2 + (24*2^n - 16)*x^2*y^3 + (12*2^n -12)*x^3*y^3 +4*x^3*y^4.
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LINKS
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Table of n, a(n) for n=0..27.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
M. Golriz, M. R. Darafsheh, and M. H. Khalifeh, The Wiener, Szeged and PI-indices of a phenylazomethine dendrimer, Digest J. Nanomaterials and Biostructures, 6, No. 4, 2011, 1545-1549.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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O.g.f.: 12*(11 + 2*x)/((1 - x)*(1 - 2*x)).
E.g.f.: 12*(-13 + 24*exp(x))*exp(x).
a(n) = 3*a(n-1) - 2*a(n-2).
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MAPLE
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seq(288*2^n-156, n = 0..35);
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MATHEMATICA
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Table[288 2^n - 156, {n, 0, 30}] (* Bruno Berselli, Nov 15 2016 *)
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PROG
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(Magma) [288*2^n-156: n in [0..40]]; // Vincenzo Librandi, Nov 15 2016
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CROSSREFS
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Cf. A278129.
Sequence in context: A205222 A116154 A305067 * A064059 A244103 A248555
Adjacent sequences: A278125 A278126 A278127 * A278129 A278130 A278131
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Nov 14 2016
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EXTENSIONS
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Edited by Bruno Berselli, Nov 15 2016
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STATUS
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approved
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