OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf 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 NS2[n] is M(NS2[n]; x,y) = 2*2^n*x*y^2 + (8*2^n - 5)*x^2*y^2 + (6*2^n - 6)*x^2*y^3.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Emeric Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
A. Madanshekaf and M. Moradi, The first geometric-arithmetic index of some nanostar dendrimers, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 15 2018: (Start)
G.f.: 2*x*(43 - 18*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2. (End)
MAPLE
seq(68*2^n-50, n = 1 .. 40);
MATHEMATICA
68*2^Range[50] - 50 (* Paolo Xausa, Jul 31 2024 *)
PROG
(GAP) List([1..40], n->68*2^n-50); # Muniru A Asiru, May 15 2018
(PARI) Vec(2*x*(43 - 18*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 15 2018
STATUS
approved