A304519 a(n) = 72*2^n -56 (n>=1).

88, 232, 520, 1096, 2248, 4552, 9160, 18376, 36808, 73672, 147400, 294856, 589768, 1179592, 2359240, 4718536, 9437128, 18874312, 37748680, 75497416, 150994888, 301989832, 603979720, 1207959496, 2415919048, 4831838152, 9663676360, 19327352776, 38654705608, 77309411272, 154618822600, 309237645256, 618475290568

Offset: 1

Author

Emeric Deutsch, May 15 2018

Keywords

• nonn
• easy

Comments

a(n) is the second Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.

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) = 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
• E. 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).

Crossrefs

Cf. A304517, A304518.

Programs

GAP

List([1..40],n->72*2^n-56); # Muniru A Asiru, May 15 2018

Maple

seq(72*2^n-56, n = 1 .. 40);

PARI

Vec(8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Formula

From Colin Barker, May 15 2018: (Start)

G.f.: 8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

(End)