OFFSET
1,1
COMMENTS
For n>=2, a(n) is the second Zagreb index of the angular phenylene shown in the Bodroza-Pantic et al. reference (Fig. 1 (b)).
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 angular phenylene A(n) is M(A(n); x, y) = (n + 4)*x^2*y^2 + 2*n*x^2*y^3 + (5*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, Fibonacci numbers and algebraic structure count of some non-benzenoid conjugated polymers, The Fibonacci Quarterly, 35, 1, 1997, 75-83.
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 24 2018: (Start)
G.f.: x*(23 + 38*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)
MAPLE
seq(61*n-38, n = 1 .. 50);
MATHEMATICA
Array[61#-38&, 50] (* Harvey P. Dale, Nov 23 2022 *)
PROG
(PARI) Vec(x*(23 + 38*x) / (1 - x)^2 + O(x^40)) \\ Colin Barker, May 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 24 2018
STATUS
approved