A304610 a(n) = 157*n - 40 (n>=1).

117, 274, 431, 588, 745, 902, 1059, 1216, 1373, 1530, 1687, 1844, 2001, 2158, 2315, 2472, 2629, 2786, 2943, 3100, 3257, 3414, 3571, 3728, 3885, 4042, 4199, 4356, 4513, 4670, 4827, 4984, 5141, 5298, 5455, 5612, 5769, 5926, 6083, 6240

Offset

1,1

Comments

a(n) is the second Zagreb index of the polymer B[n,1], 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,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.

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 18 2018: (Start)

G.f.: x*(117 + 40*x) / (1 - x)^2.

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

(End)

Maple

seq(157*n-40, n = 1 .. 40);

Mathematica

Table[157n-40, {n, 40}] (* or *) LinearRecurrence[{2, -1}, {117, 274}, 40] (* Harvey P. Dale, Oct 13 2019 *)

Prog

(GAP) List([1..40], n->157*n-40); # Muniru A Asiru, May 17 2018
(PARI) a(n) = 157*n - 40; \\ Altug Alkan, May 18 2018
(PARI) Vec(x*(117 + 40*x) / (1 - x)^2 + O(x^40)) \\ Colin Barker, May 18 2018

Crossrefs

Cf. A304609.

Sequence in context: A063332 A063338 A304611 * A298047 A252861 A252854

Adjacent sequences: A304607 A304608 A304609 * A304611 A304612 A304613

Keyword

nonn,easy

Author

Emeric Deutsch, May 17 2018

Status

approved