A304839 a(n) = 61*n - 38 (n>=1).

23, 84, 145, 206, 267, 328, 389, 450, 511, 572, 633, 694, 755, 816, 877, 938, 999, 1060, 1121, 1182, 1243, 1304, 1365, 1426, 1487, 1548, 1609, 1670, 1731, 1792, 1853, 1914, 1975, 2036, 2097, 2158, 2219, 2280, 2341, 2402, 2463, 2524, 2585, 2646, 2707, 2768, 2829, 2890, 2951, 3012

Offset: 1

Author

Emeric Deutsch, May 24 2018

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A304157.

Programs

Maple

seq(61*n-38, n = 1 .. 50);

Mathematica

Array[61#-38&,50] (* Harvey P. Dale, Nov 23 2022 *)

PARI

Vec(x*(23 + 38*x) / (1 - x)^2 + O(x^40)) \\ Colin Barker, May 24 2018

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)