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

1,1

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)

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)

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 *)

Prog

(GAP) List([1..50], n->32*n-24); # Muniru A Asiru, May 27 2018
(PARI) Vec(8*x*(1 + 3*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018

Crossrefs

Cf. A063164, A305074.

Sequence in context: A213345 A207360 A226904 * A069083 A014642 A211631

Adjacent sequences: A305072 A305073 A305074 * A305076 A305077 A305078

Keyword

nonn,easy

Author

Emeric Deutsch, May 26 2018

Status

approved