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

1,1

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).

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)

Maple

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

Prog

(GAP) List([1..50], n->20*n-8); # Muniru A Asiru, May 27 2018
(PARI) Vec(4*x*(3 + 2*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018

Crossrefs

Cf. A305075.

Sequence in context: A071336 A248817 A051519 * A166959 A134582 A177721

Adjacent sequences: A305071 A305072 A305073 * A305075 A305076 A305077

Keyword

nonn,easy

Author

Emeric Deutsch, May 26 2018

Status

approved