OFFSET

1,1

COMMENTS

a(n) is the first Zagreb index of the polymer B[n,1], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).

a(n) is the first Zagreb index of the polymer B[n,2], defined pictorially in the Bodroža-Pantić et al. reference (Fig. 4).

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 B[n,1] is M(B[n,1]; x,y) = 2*(2*n+1)*x^2*y^2 + 4*(n+1)*x^2*y^3 + (13*n-8)*x^3*y^3.

The M-polynomial of B[n,2] is M(B[n,1]; x,y) = 2*(n+2)*x^2*y^2 + 8*n*x^2*y^3 + (11*n-6)*x^3*y^3.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

O. Bodroža-Pantić, I. Gutman, and S. J. Cyvin, Algebraic structure count of some non-benzenoid conjugated polymers, ACH - Models in Chemistry, 133 (1-2), 27-41, 1996.

E. Deutsch and Sandi Klavžar, 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 (2,-1).

FORMULA

From Colin Barker, May 17 2018: (Start)

G.f.: 2*x*(47 + 10*x) / (1 - x)^2.

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

(End)

MAPLE

seq(114*n-20, n = 1 .. 40);

MATHEMATICA

114*Range[100] - 20 (* Paolo Xausa, Jul 31 2024 *)

PROG

(PARI) a(n) = 114*n - 20; \\ Altug Alkan, May 16 2018

(PARI) Vec(2*x*(47 + 10*x) / (1 - x)^2 + O(x^40)) \\ Colin Barker, May 17 2018

(GAP) List([1..80], n->114*n-20); # Muniru A Asiru, May 17 2018

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 16 2018

STATUS

approved