A304830 a(n) = 102*2^n - 108 (n>=1).

96, 300, 708, 1524, 3156, 6420, 12948, 26004, 52116, 104340, 208788, 417684, 835476, 1671060, 3342228, 6684564, 13369236, 26738580, 53477268, 106954644, 213909396, 427818900, 855637908, 1711275924, 3422551956, 6845104020, 13690208148, 27380416404, 54760832916, 109521665940, 219043331988

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

Cf. A304830.

Sequence in context: A062027 A320883 A048189 * A301459 A220540 A292345

Adjacent sequences: A304827 A304828 A304829 * A304831 A304832 A304833

Keyword

nonn,easy

Author

Emeric Deutsch, May 19 2018

Status

approved