A305066 a(n) = 234*2^n - 120.

114, 348, 816, 1752, 3624, 7368, 14856, 29832, 59784, 119688, 239496, 479112, 958344, 1916808, 3833736, 7667592, 15335304, 30670728, 61341576, 122683272, 245366664, 490733448, 981467016, 1962934152, 3925868424, 7851736968, 15703474056, 31406948232, 62813896584, 125627793288, 251255586696

Offset

0,1

Comments

a(n) is the first Zagreb index of the dendrimer nanostar G[n], defined pictorially in the Iranmanesh et al. reference (Fig. 1, where G[3] is shown) or in Alikhani et al. reference (Fig. 1, where G[3] is shown).

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 G[n] is M(G[n]; x, y) = 3*2^n*x*y^3 + (12*2^n - 6)*x^2*y^2 + (24*2^n -12)*x^2*y^3 + (9*2^n - 6)*x^3*y^3.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

S. Alikhani, M. A. Iranmanesh, Eccentric connectivity polynomials of an infinite family of dendrimer, Digest J. Nanomaterials and Biostructures, 6 (2011) 253-257.

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

A. Iranmanesh and N. Dorosti, Computing the Cluj index of a type dendrimer nanostars, MATCH Commun. Math. Comput. Chem. 65, 2011, 209-219.

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

Formula

From Colin Barker, May 25 2018: (Start)

G.f.: 6*(19 + x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2)for n>0.

(End)

Maple

seq(234*2^n-120, n = 0 .. 40);

Prog

(PARI) Vec(6*(19 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 25 2018

Crossrefs

Cf. A305064, A305065, A305067.

Sequence in context: A228962 A250725 A300478 * A322541 A323758 A043403

Adjacent sequences: A305063 A305064 A305065 * A305067 A305068 A305069

Keyword

nonn,easy

Author

Emeric Deutsch, May 25 2018

Status

approved