A305069 a(n) = 117*n - 72 (n>=1).

45, 162, 279, 396, 513, 630, 747, 864, 981, 1098, 1215, 1332, 1449, 1566, 1683, 1800, 1917, 2034, 2151, 2268, 2385, 2502, 2619, 2736, 2853, 2970, 3087, 3204, 3321, 3438, 3555, 3672, 3789, 3906, 4023, 4140, 4257, 4374, 4491, 4608, 4725, 4842, 4959, 5076, 5193, 5310, 5427, 5544, 5661, 5778

Offset

1,1

Comments

a(n) is the second Zagreb index of the chain silicate network CS(n), defined pictorially in the Javaid et al. reference (Fig. 2, where CS(6) is shown) or in Liu et al. reference (Fig. 4, where CS(8) 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 CS(n) is M(C(n); x, y) = (n+4)*x^3*y^3 + (4*n-2)*x^3*y^6 + (n-2)*x^6*y^6 (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.

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 (2,-1).

Formula

From Colin Barker, May 26 2018: (Start)

G.f.: 9*x*(5 + 8*x) / (1 - x)^2.

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

(End)

Maple

seq(117*n-72, n = 1 .. 50);

Prog

(PARI) Vec(9*x*(5 + 8*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 26 2018
(GAP) List([1..50], n->117*n-72); # Muniru A Asiru, May 27 2018

Crossrefs

Cf. A305068.

Sequence in context: A234336 A173371 A288669 * A061658 A254147 A271737

Adjacent sequences: A305066 A305067 A305068 * A305070 A305071 A305072

Keyword

nonn,easy

Author

Emeric Deutsch, May 25 2018

Status

approved