A304387 a(n) = 27*2^n - 5.

22, 49, 103, 211, 427, 859, 1723, 3451, 6907, 13819, 27643, 55291, 110587, 221179, 442363, 884731, 1769467, 3538939, 7077883, 14155771, 28311547, 56623099, 113246203, 226492411, 452984827, 905969659, 1811939323, 3623878651, 7247757307, 14495514619, 28991029243, 57982058491

Offset

0,1

Comments

For n>0, a(n) is the number of edges in the dendrimer nanostar NS1[n] defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).

Links

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

M. B. Ahmadi and M. Sadeghimehr, Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.

Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.

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

Formula

From Colin Barker, May 18 2018: (Start)

G.f.: (22 - 17*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(27*2^n-5, n = 0 .. 40);

Mathematica

27*2^Range[0, 40]-5 (* or *) LinearRecurrence[{3, -2}, {22, 49}, 40] (* Harvey P. Dale, Jan 12 2019 *)

Prog

(PARI) a(n) = 27*2^n - 5; \\ Altug Alkan, May 13 2018
(PARI) Vec((22 - 17*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018
(GAP) List([1..40], n->27*2^n-5); # Muniru A Asiru, May 13 2018

Crossrefs

Cf. A304386, A250653.

Sequence in context: A217751 A209186 A085381 * A039345 A043168 A043948

Adjacent sequences: A304384 A304385 A304386 * A304388 A304389 A304390

Keyword

nonn,easy

Author

Emeric Deutsch, May 13 2018

Extensions

Offset changed by N. J. A. Sloane, May 13 2018

Status

approved