A305075 a(n) = 32*n - 24 (n>=1).

8, 40, 72, 104, 136, 168, 200, 232, 264, 296, 328, 360, 392, 424, 456, 488, 520, 552, 584, 616, 648, 680, 712, 744, 776, 808, 840, 872, 904, 936, 968, 1000, 1032, 1064, 1096, 1128, 1160, 1192, 1224, 1256, 1288, 1320, 1352, 1384, 1416, 1448, 1480, 1512, 1544, 1576

Offset: 1

Author

Emeric Deutsch, May 26 2018

Keywords

• nonn
• easy

Comments

a(n) (n>=2) is the second 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 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 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
• 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. A063164, A305074.

Programs

GAP

List([1..50], n->32*n-24); # Muniru A Asiru, May 27 2018

Maple

seq(32*n - 24, n = 1 .. 50);

Mathematica

32*Range[60]-24 (* or *) LinearRecurrence[{2,-1},{8,40},60] (* Harvey P. Dale, Mar 13 2022 *)

PARI

Vec(8*x*(1 + 3*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018

Formula

a(n) = A063164(n) for n > 1.

From Colin Barker, May 29 2018: (Start)

G.f.: 8*x*(1 + 3*x) / (1 - x)^2.

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

(End)