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A224435
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The Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference.
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2
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1248, 136272, 1590360, 11608536, 69325368, 371933112, 1870634040, 9019095096, 42224645688, 193479671352, 872186750520, 3881641715256, 17097660401208, 74673784423992, 323824724575800, 1395810233321016, 5985270160655928, 25549161151039032, 108628885484045880
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OFFSET
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0,1
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COMMENTS
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a(0) has been checked by the direct computation of the Wiener index (using Maple).
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
N. E. Arif, Roslan Hasni and Saeid Alikhani, Fourth order and fourth sum connectivity indices of polyphenylene dendrimers, J. Applied Science, 12 (21), 2012, 2279-2282.
Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64).
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FORMULA
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a(n) = -31176 + 136464*2^n + 93600*n*4^n - 31860*n*2^n - 104040*4^n.
G.f.: 24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4)/((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2).
a(n) = 13*a(n-1) - 64*a(n-2) + 148*a(n-3) - 160*a(n-4) + 64*a(n-5) for n>4.
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MAPLE
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a := proc (n) options operator, arrow: -31176+136464*2^n+93600*4^n*n-31860*2^n*n-104040*4^n end proc: seq(a(n), n = 0 .. 18);
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PROG
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(PARI) Vec(24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4) / ((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2) + O(x^50)) \\ Colin Barker, May 30 2018
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CROSSREFS
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Cf. A224436.
Sequence in context: A233167 A266037 A233179 * A233261 A233201 A233244
Adjacent sequences: A224432 A224433 A224434 * A224436 A224437 A224438
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Apr 06 2013
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STATUS
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approved
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