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A305269 a(n) = 120*2^n - 95. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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).

LINKS

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 (3,-2).

FORMULA

From Colin Barker, May 31 2018: (Start)

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)

MAPLE

seq(120*2^n-95, n = 0..40);

PROG

(PARI) Vec(5*(5 + 14*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

CROSSREFS

Cf. A305270, A305271, A305272.

Sequence in context: A072471 A017042 A100255 * A052501 A193438 A139152

Adjacent sequences:  A305266 A305267 A305268 * A305270 A305271 A305272

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 30 2018

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)