A305062 - OEIS

A305062

a(n) = 96*2^n + 80.

176, 272, 464, 848, 1616, 3152, 6224, 12368, 24656, 49232, 98384, 196688, 393296, 786512, 1572944, 3145808, 6291536, 12582992, 25165904, 50331728, 100663376, 201326672, 402653264, 805306448, 1610612816, 3221225552, 6442451024, 12884901968, 25769803856, 51539607632, 103079215184, 206158430288, 412316860496, 824633720912, 1649267441744

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OFFSET

0,1

COMMENTS

a(n) (n>=0) is the first Zagreb index of the dendrimer graph K[n], defined pictorially in the Ghorbani et al. reference (see Figs. 9, 10, and 11).

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 K[n] is M(K[n];x,y) = 2*2^n*x*y^3 + 2*(2^n + 2)*x^2*y^2 + (2^4*2^n -4)*x^2*y^3 + 14*x^3*y^3.

LINKS

Table of n, a(n) for n=0..34.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

M. Ghorbani, K. Malekjani, and A. Khaki, Eccentric connectivity index of some dendrimer graphs, Iranian J. of Math. Chemistry, 3, Supplement 1, 2012, s7 - s18.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

G.f.: (176 - 256*x)/((1 - 2*x)*(1 - x)). - Vincenzo Librandi, May 25 2018

a(n) = 3*a(n-1) - 2*a(n-2). - Vincenzo Librandi, May 25 2018

MAPLE

seq(96*2^n+80, n = 0 .. 40);

MATHEMATICA

Table[96 2^n + 80, {n, 0, 30}] (* Vincenzo Librandi, May 25 2018 *)

PROG

(Magma) [96*2^n+80: n in [0..40]]; // Vincenzo Librandi, May 25 2018

CROSSREFS

Cf. A305060, A305061, A305063.