A305064 a(n) = 42*2^n - 20.

22, 64, 148, 316, 652, 1324, 2668, 5356, 10732, 21484, 42988, 85996, 172012, 344044, 688108, 1376236, 2752492, 5505004, 11010028, 22020076, 44040172, 88080364, 176160748, 352321516, 704643052, 1409286124, 2818572268, 5637144556, 11274289132, 22548578284, 45097156588, 90194313196, 180388626412, 360777252844

Offset

0,1

Comments

a(n) is the number of vertices in 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).

Links

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

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.: 2*(11 - x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(42*2^n-20, n = 0 .. 40);

Prog

(PARI) Vec(2*(11 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 25 2018

Crossrefs

Cf. A305065, A305066, A305067.

Sequence in context: A140390 A069178 A081929 * A124715 A126376 A136604

Adjacent sequences: A305061 A305062 A305063 * A305065 A305066 A305067

Keyword

nonn,easy

Author

Emeric Deutsch, May 25 2018

Status

approved