A305073 a(n) = 288*n^2 - 96*n (n>=1).

192, 960, 2304, 4224, 6720, 9792, 13440, 17664, 22464, 27840, 33792, 40320, 47424, 55104, 63360, 72192, 81600, 91584, 102144, 113280, 124992, 137280, 150144, 163584, 177600, 192192, 207360, 223104, 239424, 256320, 273792, 291840, 310464, 329664, 349440, 369792, 390720, 412224, 434304, 456960, 480192, 504000

Offset

1,1

Comments

a(n) is the second Zagreb index of the oxide network OX(n), defined pictorially in the Javaid et al. reference (Fig. 3, where OX(2) is shown) or in Liu et al. reference (Fig. 6, where OX(5) is shown).

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 OX(n) is M(OX(n); x, y) = 12*n*x^2*y^4 + 6*n*(3*n - 2)*x^4*y^4 (n>=1).

a(n)/8 + 1 is a square. - Muniru A Asiru, May 27 2018

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.

M. Javaid and C. Y. Jung, M-polynomials and topological indices of silicate and oxide networks, International J. Pure and Applied Math., 115, No. 1, 2017, 129-152.

J.-B. Liu, S. Wang, C. Wang, and S. Hayat, Further results on computation of topological indices of certain networks, IET Control Theory Appl., 11, No. 13, 2017, 2065-2071.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, May 26 2018: (Start)

G.f.: 192*x*(1 + 2*x) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

Maple

seq(288*n^2 - 96*n, n = 1 .. 50);

Prog

(PARI) Vec(192*x*(1 + 2*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, May 26 2018
(GAP) List([1..50], n->288*n^2-96*n); # Muniru A Asiru, May 27 2018

Crossrefs

Cf. A305072.

Sequence in context: A194647 A054001 A051527 * A101451 A094949 A205768

Adjacent sequences: A305070 A305071 A305072 * A305074 A305075 A305076

Keyword

nonn,easy

Author

Emeric Deutsch, May 26 2018

Status

approved