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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 29 2018
STATUS
approved