A304384 a(n) = 168*2^n - 26 (n>=1).

310, 646, 1318, 2662, 5350, 10726, 21478, 42982, 85990, 172006, 344038, 688102, 1376230, 2752486, 5504998, 11010022, 22020070, 44040166, 88080358, 176160742, 352321510, 704643046, 1409286118, 2818572262, 5637144550, 11274289126, 22548578278, 45097156582, 90194313190

Offset

1,1

Comments

a(n) is the first Zagreb index of the molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).

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 NS2[n] is M(NS2[n]; x,y) = (12*2^n + 2)x^2*y^2 + (24*2^n - 8)x^2*y^3 + x^3*y^3.

Links

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

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).

Formula

From Colin Barker, May 14 2018: (Start)

G.f.: 2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(168*2^n-26, n = 1 .. 40);

Prog

(GAP) List([1..40], n->168*2^n-26); # Muniru A Asiru, May 13 2018
(PARI) Vec(2*x*(155 - 142*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 14 2018

Crossrefs

Cf. A304385.

Sequence in context: A273593 A051981 A134549 * A206233 A254972 A237697

Adjacent sequences: A304381 A304382 A304383 * A304385 A304386 A304387

Keyword

nonn,easy

Author

Emeric Deutsch, May 13 2018

Status

approved