A305158 a(n) = 21*2^n - 15.

6, 27, 69, 153, 321, 657, 1329, 2673, 5361, 10737, 21489, 42993, 86001, 172017, 344049, 688113, 1376241, 2752497, 5505009, 11010033, 22020081, 44040177, 88080369, 176160753, 352321521, 704643057, 1409286129, 2818572273, 5637144561, 11274289137, 22548578289, 45097156593, 90194313201, 180388626417

Offset

0,1

Comments

a(n) is the number of edges of the all-aromatic dendrimer G[n], shown pictorially as DNS1[n] in the Shabani et al. reference (Fig. 1).

Links

Muniru A Asiru, Table of n, a(n) for n = 0..700

H. Shabani, A. R. Ashrafi, and I. Gutman, Geometric-arithmetic index: an algebraic approach, Studia UBB, Chemia, 55, No. 4, 107-112, 2010.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Colin Barker, May 30 2018: (Start)

G.f.: 3*(2 + 3*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

(End)

Maple

seq(21*2^n-15, n = 0..40);

Mathematica

21*2^Range[0, 40]-15 (* or *) LinearRecurrence[{3, -2}, {6, 27}, 40] (* Harvey P. Dale, Apr 15 2019 *)

Prog

(GAP) List([0..40], n->21*2^n-15); # Muniru A Asiru, May 30 2018
(PARI) Vec(3*(2 + 3*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A305159, A305160.

Sequence in context: A363696 A167469 A190623 * A273408 A085788 A027276

Adjacent sequences: A305155 A305156 A305157 * A305159 A305160 A305161

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved