A304611 a(n) = 155*n - 38.

117, 272, 427, 582, 737, 892, 1047, 1202, 1357, 1512, 1667, 1822, 1977, 2132, 2287, 2442, 2597, 2752, 2907, 3062, 3217, 3372, 3527, 3682, 3837, 3992, 4147, 4302, 4457, 4612, 4767, 4922, 5077, 5232, 5387, 5542, 5697, 5852, 6007, 6162, 6317, 6472, 6627, 6782, 6937, 7092, 7247, 7402, 7557, 7712

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

Cf. A304609.

Sequence in context: A146189 A063332 A063338 * A304610 A298047 A252861

Adjacent sequences: A304608 A304609 A304610 * A304612 A304613 A304614

Keyword

nonn,easy

Author

Emeric Deutsch, May 24 2018

Status

approved