A305067 a(n) = 282*2^n - 150.

132, 414, 978, 2106, 4362, 8874, 17898, 35946, 72042, 144234, 288618, 577386, 1154922, 2309994, 4620138, 9240426, 18481002, 36962154, 73924458, 147849066, 295698282, 591396714, 1182793578, 2365587306, 4731174762, 9462349674, 18924699498, 37849399146, 75698798442, 151397597034

Offset

0,1

Comments

a(n) is the second Zagreb index of the dendrimer nanostar G[n], defined pictorially in the Iranmanesh et al. reference (Fig. 1, where G[3] is shown) or in Alikhani et al. reference (Fig. 1, where G[3] 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 G[n] is M(G[n]; x, y) = 3*2^n*x*y^3 + (12*2^n - 6)*x^2*y^2 + (24*2^n -12)*x^2*y^3 + (9*2^n - 6)*x^3*y^3.

Links

Muniru A Asiru, Table of n, a(n) for n = 0..600

S. Alikhani, M. A. Iranmanesh, Eccentric connectivity polynomials of an infinite family of dendrimer, Digest J. Nanomaterials and Biostructures, 6 (2011) 253-257.

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

A. Iranmanesh and N. Dorosti, Computing the Cluj index of a type dendrimer nanostars, MATCH Commun. Math. Comput. Chem. 65, 2011, 209-219.

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

Formula

From Colin Barker, May 25 2018: (Start)

G.f.: 6*x*(22 + 3*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(282*2^n - 150, n = 0 .. 40);

Mathematica

282*2^Range[0, 30]-150 (* or *) LinearRecurrence[{3, -2}, {132, 414}, 30] (* Harvey P. Dale, Apr 09 2023 *)

Prog

(PARI) Vec(6*x*(22 + 3*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 25 2018
(GAP) List([0..50], n->282*2^n-150); # Muniru A Asiru, May 27 2018

Crossrefs

Cf. A305064, A305065, A305066.

Sequence in context: A035141 A205222 A116154 * A278128 A064059 A244103

Adjacent sequences: A305064 A305065 A305066 * A305068 A305069 A305070

Keyword

nonn,easy

Author

Emeric Deutsch, May 25 2018

Status

approved