A278129 a(n) = 348*2^n - 188.

160, 508, 1204, 2596, 5380, 10948, 22084, 44356, 88900, 177988, 356164, 712516, 1425220, 2850628, 5701444, 11403076, 22806340, 45612868, 91225924, 182452036, 364904260, 729808708, 1459617604, 2919235396, 5838470980, 11676942148, 23353884484

Offset

0,1

Comments

a(n) is the second Zagreb index of the phenylazomethine dendrimer G[n], defined pictorially in the Golriz et al. reference (Fig. 1). 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 the dendrimer G[n] is M(G[n],x,y) = (24*2^n - 8)*x^2*y^2 + (24*2^n - 16)*x^2*y^3 + (12*2^n -12)*x^3*y^3 +4*x^3*y^4.

Links

Table of n, a(n) for n=0..26.

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

M. Golriz, M. R. Darafsheh, and M. H. Khalifeh, The Wiener, Szeged and PI-indices of a phenylazomethine dendrimer, Digest J. Nanomaterials and Biostructures, 6, No. 4, 2011, 1545-1549.

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

Formula

O.g.f.: 4*(40 + 7*x)/((1 - x)*(1 - 2*x)).

E.g.f.: 4*(-47 + 87*exp(x))*exp(x).

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

Maple

seq(348*2^n-188, n = 0..35);

Mathematica

Table[348 2^n - 188, {n, 0, 30}] (* Bruno Berselli, Nov 15 2016 *)
LinearRecurrence[{3, -2}, {160, 508}, 30] (* Harvey P. Dale, Jul 22 2021 *)

Prog

(Magma) [348*2^n-188: n in [0..40]]; // Vincenzo Librandi, Nov 15 2016

Crossrefs

Cf. A278128.

Sequence in context: A127338 A138854 A133530 * A184070 A278122 A233917

Adjacent sequences: A278126 A278127 A278128 * A278130 A278131 A278132

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 15 2016

Status

approved