A305063 a(n) = 110*2^n + 118.

228, 338, 558, 998, 1878, 3638, 7158, 14198, 28278, 56438, 112758, 225398, 450678, 901238, 1802358, 3604598, 7209078, 14418038, 28835958, 57671798, 115343478, 230686838, 461373558, 922746998, 1845493878, 3690987638, 7381975158, 14763950198, 29527900278, 59055800438, 118111600758, 236223201398

Offset

0,1

Comments

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

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 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..31.

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.: (228 - 346*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(110*2^n+118, n = 0 .. 40);

Mathematica

Table[110 2^n + 118, {n, 0, 31}] (* Vincenzo Librandi, May 25 2018 *)

Prog

(Magma) [110*2^n+118: n in [0..40]]; // Vincenzo Librandi, May 25 2018

Crossrefs

Cf. A305060, A305061, A305062.

Sequence in context: A190027 A090943 A252451 * A258550 A335269 A252228

Adjacent sequences: A305060 A305061 A305062 * A305064 A305065 A305066

Keyword

nonn,easy

Author

Emeric Deutsch, May 24 2018

Status

approved