A304518 a(n) = 68*2^n - 50 (n>=1).

86, 222, 494, 1038, 2126, 4302, 8654, 17358, 34766, 69582, 139214, 278478, 557006, 1114062, 2228174, 4456398, 8912846, 17825742, 35651534, 71303118, 142606286, 285212622, 570425294, 1140850638, 2281701326, 4563402702, 9126805454, 18253610958, 36507221966, 73014443982, 146028888014, 292057776078, 584115552206, 1168231104462

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

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).

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);

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

Cf. A304517, A304519.

Sequence in context: A184095 A097693 A184087 * A306112 A184086 A113690

Adjacent sequences: A304515 A304516 A304517 * A304519 A304520 A304521

Keyword

nonn,easy

Author

Emeric Deutsch, May 15 2018

Status

approved