OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).
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 NS2[n] is M(NS2[n]; x,y) = (12*2^n + 2)*x^2*y^2 + (24*2^n - 8)*x^2*y^3 + x^3*y^3.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 14 2018: (Start)
G.f.: x*(353 - 322*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(192*2^n-31, n = 1 .. 40);
PROG
(GAP) List([1..40], n->192*2^n-31); # Muniru A Asiru, May 13 2018
(PARI) Vec(x*(353 - 322*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 14 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 13 2018
STATUS
approved