OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the dendrimer molecule D[n] defined in the Ashrafi 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 the dendrimer molecule D[n] is M(D[n]; x,y) = 6*2^n*x^2*y^2 + 6(2*2^n - 3)*x^2*y^3 + 3*(2^n - 1)*x^3*y^3.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..700
A. R. Ashrafi, H. Shabani, M. V. Diudea, Balaban index of dendrimers, MATCH, Commun. Math. Comput. Chem. 69, 2013, 151-158.
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 20 2018: (Start)
G.f.: 12*x*(8 + x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(102*2^n-108, n = 1 .. 35);
MATHEMATICA
Table[102*2^n-108, {n, 40}] (* or *) LinearRecurrence[{3, -2}, {96, 300}, 40] (* Harvey P. Dale, Jan 07 2022 *)
PROG
(GAP) List([1..40], n->102*2^n-108); # Muniru A Asiru, May 19 2018
(PARI) Vec(12*x*(8 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 19 2018
STATUS
approved