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A305265
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a(n) = 12*2^n + 62.
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4
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74, 86, 110, 158, 254, 446, 830, 1598, 3134, 6206, 12350, 24638, 49214, 98366, 196670, 393278, 786494, 1572926, 3145790, 6291518, 12582974, 25165886, 50331710, 100663358, 201326654, 402653246, 805306430, 1610612798, 3221225534, 6442451006, 12884901950, 25769803838, 51539607614, 103079215166, 206158430270
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OFFSET
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0,1
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COMMENTS
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a(n) (n>=1) is the number of vertices of the first type of dendrimer nanostar G[n], shown pictorially in the Iranmanesh et al. reference (Fig. 1).
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LINKS
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FORMULA
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G.f.: 2*(37 - 68*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(12*2^n+62, n = 0..40);
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MATHEMATICA
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Table[12*2^n+62, {n, 0, 50}] (* or *) LinearRecurrence[{3, -2}, {74, 86}, 50] (* Harvey P. Dale, Jun 23 2020 *)
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PROG
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(PARI) Vec(2*(37 - 68*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 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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