OFFSET
0,1
COMMENTS
a(n) is the second Zagreb index of the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).
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 nanostar dendrimer G[n] is M(G[n]; x, y) = (56*2^n - 48)*x^2*y^2 + (48*2^n - 44)*x^2*y^3 +(36* 2^n - 35)*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.
M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 31 2018: (Start)
G.f.: (65 + 706*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(836*2^n-771, n = 0..40);
PROG
(PARI) Vec((65 + 706*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 29 2018
STATUS
approved