OFFSET
0,1
COMMENTS
a(n) is the second Zagreb index of the all-aromatic dendrimer G[n], shown pictorially as DNS1[n] in the Shabani et al. reference (Fig. 1).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of the dendrimer G[n] is M(G[n]; x, y) = 6*2^n*x^2*y^2 + 12*(2^n - 1)*x^2*y^3 +3* (2^n - 1)*x^3*y^3.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
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*(8 + 25*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(123*2^n-99, n = 0..40);
MATHEMATICA
123*2^Range[0, 40]-99 (* or *) LinearRecurrence[{3, -2}, {24, 147}, 40] (* Harvey P. Dale, Aug 14 2021 *)
PROG
(PARI) Vec(3*(8 + 25*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