A305159 a(n) = 102*2^n - 78.

24, 126, 330, 738, 1554, 3186, 6450, 12978, 26034, 52146, 104370, 208818, 417714, 835506, 1671090, 3342258, 6684594, 13369266, 26738610, 53477298, 106954674, 213909426, 427818930, 855637938, 1711275954, 3422551986, 6845104050, 13690208178, 27380416434, 54760832946, 109521665970, 219043332018

Offset

0,1

Comments

a(n) is the first Zagreb index of the all-aromatic dendrimer G[n], shown pictorially as DNS1[n] in the Shabani 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 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

Muniru A Asiru, 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.: 6*(4 + 9*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(102*2^n-78, n = 0..40);

Prog

(GAP) List([0..40], n->102*2^n-78); # Muniru A Asiru, May 30 2018
(PARI) Vec(6*(4 + 9*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A305158, A305160.

Sequence in context: A244794 A044356 A044737 * A326367 A182186 A188304

Adjacent sequences: A305156 A305157 A305158 * A305160 A305161 A305162

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved