A305264 a(n) = 836*2^n - 771.

65, 901, 2573, 5917, 12605, 25981, 52733, 106237, 213245, 427261, 855293, 1711357, 3423485, 6847741, 13696253, 27393277, 54787325, 109575421, 219151613, 438303997, 876608765, 1753218301, 3506437373, 7012875517, 14025751805, 28051504381, 56103009533, 112206019837, 224412040445, 448824081661, 897648164093, 1795296328957

Offset

0,1

Comments

a(n) is the second Zagreb index of the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).

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 the nanostar dendrimer G[n] is M(G[n]; x, y) = (56*2^n - 48)*x^2*y^2 + (48*2^n - 44)*x^2*y^3 +(36* 2^n - 35)*x^3*y^3.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Colin Barker, May 31 2018: (Start)

G.f.: (65 + 706*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(836*2^n-771, n = 0..40);

Prog

(PARI) Vec((65 + 706*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

Crossrefs

Cf. A305261, A305262, A305263.

Sequence in context: A023875 A301550 A027463 * A279639 A144500 A086021

Adjacent sequences: A305261 A305262 A305263 * A305265 A305266 A305267

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved