A305074 a(n) = 20*n - 8 (n>=1).

12, 32, 52, 72, 92, 112, 132, 152, 172, 192, 212, 232, 252, 272, 292, 312, 332, 352, 372, 392, 412, 432, 452, 472, 492, 512, 532, 552, 572, 592, 612, 632, 652, 672, 692, 712, 732, 752, 772, 792, 812, 832, 852, 872, 892, 912, 932, 952, 972, 992

Offset: 1

Author

Emeric Deutsch, May 26 2018

Keywords

• nonn
• easy

Comments

a(n) is the first Zagreb index of the single oxide chain SOX(n), defined pictorially in the Simonraj et al. reference (Fig. 4, where SOX(9) is shown, marked as OX(1,9)).

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.

The M-polynomial of SL(n) is M(SL(n); x, y) = 2*x^2*y^2 + 2*n*x^2*y^4 + (n - 2)*x^4*y^4 (n>=2).

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000
• E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
• F. Simonraj and A. George, Topological properties of few poly oxide, poly silicate, DOX and DSL networks, International J. of Future Computer and Communication, 2, No. 2, 2013, 90-95.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A305075.

Programs

GAP

List([1..50], n->20*n-8); # Muniru A Asiru, May 27 2018

Maple

seq(-8+20*n, n = 1 .. 50);

PARI

Vec(4*x*(3 + 2*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018

Formula

From Colin Barker, May 29 2018: (Start)

G.f.: 4*x*(3 + 2*x) / (1 - x)^2.

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

(End)