A304389 a(n) = 126*2^n - 22 (n>=1).

230, 482, 986, 1994, 4010, 8042, 16106, 32234, 64490, 129002, 258026, 516074, 1032170, 2064362, 4128746, 8257514, 16515050, 33030122, 66060266, 132120554, 264241130, 528482282, 1056964586, 2113929194, 4227858410, 8455716842, 16911433706, 33822867434, 67645734890, 135291469802, 270582939626, 541165879274

Offset: 1

Author

Emeric Deutsch, May 13 2018

Keywords

• nonn
• easy

Comments

a(n) is the first Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.

The M-polynomial of NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n + 3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4 .

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• M. B. Ahmadi and M. Sadeghimehr, Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
• Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
• E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A304386, A304387, A304388.

Programs

GAP

List([1..40],n->126*2^n-22); # Muniru A Asiru, May 13 2018

Maple

seq(126*2^n-22, n = 1 .. 40);

PARI

a(n) = 126*2^n - 22; \\ Altug Alkan, May 13 2018

PARI

Vec(2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018

Formula

From Colin Barker, May 18 2018: (Start)

G.f.: 2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)).

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

(End)