A305071 a(n) = 972*n^2 - 270*n (n>=1).

702, 3348, 7938, 14472, 22950, 33372, 45738, 60048, 76302, 94500, 114642, 136728, 160758, 186732, 214650, 244512, 276318, 310068, 345762, 383400, 422982, 464508, 507978, 553392, 600750, 650052, 701298, 754488, 809622, 866700, 925722, 986688, 1049598, 1114452, 1181250, 1249992, 1320678, 1393308, 1467882, 1544400

Offset

1,1

Comments

a(n) is the second Zagreb index of the silicate network SL(n), defined pictorially in the Javaid et al. reference (Fig. 1, where SL(2) is shown) or in Liu et al. reference (Fig. 3, where again SL(2) 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 SL(n) is M(SL(n); x, y) = 6*n*x^3*y^3 + (18*n^2 + 6*n)*x^3*y^6 + (18*n^2 -12*n)*x^6*y^6 (n>=2).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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.: 54*x*(13 + 23*x) / (1 - x)^3.

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

(End)

Maple

seq(972*n^2-270*n, n = 1..50);

Prog

(PARI) Vec(54*x*(13 + 23*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, May 26 2018
(GAP) List([1..40], n->972*n^2-270*n); # Muniru A Asiru, May 30 2018

Crossrefs

Cf. A305070.

Sequence in context: A305174 A316762 A158655 * A203350 A321641 A304064

Adjacent sequences: A305068 A305069 A305070 * A305072 A305073 A305074

Keyword

nonn,easy

Author

Emeric Deutsch, May 25 2018

Status

approved