OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the polymer B(n,2), defined pictorially in the Bodroza-Pantic et al. reference (Fig. 4).
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 B[n,2] is M(B[n,2]; 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. Bodroza-Pantic, 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 Klavzar, 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 29 2018: (Start)
G.f.: x*(117 + 38*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)
MAPLE
seq(155*n-38, n = 1 .. 50);
PROG
(PARI) Vec(x*(117 + 38*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 24 2018
STATUS
approved