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A305269
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a(n) = 120*2^n - 95.
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4
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25, 145, 385, 865, 1825, 3745, 7585, 15265, 30625, 61345, 122785, 245665, 491425, 982945, 1965985, 3932065, 7864225, 15728545, 31457185, 62914465, 125829025, 251658145, 503316385, 1006632865, 2013265825, 4026531745, 8053063585, 16106127265, 32212254625, 64424509345, 128849018785
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OFFSET
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0,1
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COMMENTS
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a(n) is the number of vertices in the polyphenylene dendrimer G[n], defined pictorially in the Arif et al. reference (see Fig. 1, where G[2] is shown).
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LINKS
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FORMULA
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G.f.: 5*(5 + 14*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(120*2^n-95, n = 0..40);
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PROG
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(PARI) Vec(5*(5 + 14*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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