OFFSET
0,1
COMMENTS
a(n) is the first Zagreb index of the dendrimer D[n], defined pictorially in Fig. 1 of the Heydari et al. reference.
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of D[n] is M(D[n];x,y) = 3*2^n*x*y^3 + 6*x^2*y^3 + 3*(2^n - 1)*x^3*y^3 (n>=0).
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.
A. Heydari and I. Gutman, On the terminal Wiener index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 29 2018: (Start)
G.f.: 6*(7 - 9*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(30*2^n+12, n = 0..40);
PROG
(PARI) Vec(6*(7 - 9*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 27 2018
STATUS
approved