A305262 a(n) = 140*2^n - 127.

13, 153, 433, 993, 2113, 4353, 8833, 17793, 35713, 71553, 143233, 286593, 573313, 1146753, 2293633, 4587393, 9174913, 18349953, 36700033, 73400193, 146800513, 293601153, 587202433, 1174404993, 2348810113, 4697620353, 9395240833, 18790481793, 37580963713, 75161927553, 150323855233

Offset

0,1

Comments

a(n) is the number of edges of the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).

Links

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

M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, Vol. 7, No. 1 (2012), 247-252.

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

Formula

From Colin Barker, May 31 2018: (Start)

G.f.: (13 + 114*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(140*2^n-127, n = 0 .. 40);

Mathematica

Table[140*2^n-127, {n, 0, 40}] (* Harvey P. Dale, Nov 23 2024 *)
(* Alternative: *)
LinearRecurrence[{3, -2}, {13, 153}, 40] (* Harvey P. Dale, Nov 23 2024 *)

Prog

(PARI) a(n) = 140*2^n - 127 \\ Felix Fröhlich, May 29 2018
(PARI) Vec((13 + 114*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

Crossrefs

Cf. A305261, A305263, A305264.

Sequence in context: A396245 A097168 A382516 * A296722 A252972 A108366

Adjacent sequences: A305259 A305260 A305261 * A305263 A305264 A305265

Keyword

nonn,easy,changed

Author

Emeric Deutsch, May 29 2018

Status

approved