A305160 a(n) = 123*2^n - 99.

24, 147, 393, 885, 1869, 3837, 7773, 15645, 31389, 62877, 125853, 251805, 503709, 1007517, 2015133, 4030365, 8060829, 16121757, 32243613, 64487325, 128974749, 257949597, 515899293, 1031798685, 2063597469, 4127195037, 8254390173, 16508780445, 33017560989, 66035122077, 132070244253, 264140488605

Offset

0,1

Comments

a(n) is the second Zagreb index of the all-aromatic dendrimer G[n], shown pictorially as DNS1[n] in the Shabani et al. reference (Fig. 1).

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 dendrimer G[n] is M(G[n]; x, y) = 6*2^n*x^2*y^2 + 12*(2^n - 1)*x^2*y^3 +3* (2^n - 1)*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.

H. Shabani, A. R. Ashrafi, and I. Gutman, Geometric-arithmetic index: an algebraic approach, Studia UBB, Chemia, 55, No. 4, 107-112, 2010.

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

Formula

From Colin Barker, May 30 2018: (Start)

G.f.: 3*(8 + 25*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(123*2^n-99, n = 0..40);

Mathematica

123*2^Range[0, 40]-99 (* or *) LinearRecurrence[{3, -2}, {24, 147}, 40] (* Harvey P. Dale, Aug 14 2021 *)

Prog

(PARI) Vec(3*(8 + 25*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A305158, A305159.

Sequence in context: A042118 A039494 A159650 * A279459 A092181 A001702

Adjacent sequences: A305157 A305158 A305159 * A305161 A305162 A305163

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved