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A305265
a(n) = 12*2^n + 62.
4
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
OFFSET
0,1
COMMENTS
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).
LINKS
A. Iranmanesh, N. A. Gholami, Computing the Szeged index of two type dendrimer nanostars, Croatica Chemica Acta, 81, No. 2, 2008, 299-303.
FORMULA
From Colin Barker, May 30 2018: (Start)
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)
MAPLE
seq(12*2^n+62, n = 0..40);
MATHEMATICA
Table[12*2^n+62, {n, 0, 50}] (* or *) LinearRecurrence[{3, -2}, {74, 86}, 50] (* Harvey P. Dale, Jun 23 2020 *)
PROG
(PARI) Vec(2*(37 - 68*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 29 2018
STATUS
approved