A013731 a(n) = 2^(3*n+2).

4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936, 576460752303423488, 4611686018427387904

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Starting rank of the (j-1)-Washtenaw series for the fixed ratio 2^(-j-1) (see Griess). - J. Taylor (jt_cpp(AT)yahoo.com), Apr 03 2004

1/4 + 1/32 + 1/256 + 1/2048 + ... = 2/7. - Gary W. Adamson, Aug 29 2008

Independence number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Sep 06 2017

Clique covering number of the (n+1)-Sierpinski carpet graph. - Eric W. Weisstein, Apr 22 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Robert L. Griess Jr. Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices, arXiv:math/0403480 [math.GR], Mar 28 2004. See Definition 14.21.
• Tanya Khovanova, Recursive Sequences
• Eric Weisstein's World of Mathematics, Clique Covering Number
• Eric Weisstein's World of Mathematics, Independence Number
• Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (8).

Crossrefs

Cf. A001018, A013730, A198852.

Cf. A092811 (same sequence with 1 prepended).

Programs

Magma

[2^(3*n+2): n in [0..20]]; // Vincenzo Librandi, Jun 26 2011

Maple

seq(2^(3*n+2),n=0..19); # Nathaniel Johnston, Jun 26 2011

Mathematica

(* Start from Eric W. Weisstein, Sep 06 2017 *)
Table[2^(3 n + 2), {n, 0, 20}]
2^(3 Range[0, 20] + 2)
LinearRecurrence[{8}, {4}, 20]
CoefficientList[Series[-(4/(-1 + 8 x)), {x, 0, 20}], x]
(* End *)

PARI

a(n)=4<<(3*n) \\ Charles R Greathouse IV, Apr 07 2012

Sage

[lucas_number1(3*n, 2, 0) for n in range(1, 20)] # Zerinvary Lajos, Oct 27 2009

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 8*a(n-1), n > 0; a(0)=4.

G.f.: 4/(1-8x). (End)

a(n) = A198852(n) + 1. - Michel Marcus, Aug 23 2013

a(n) = A092811(n+1). - Eric W. Weisstein, Sep 06 2017

a(n) = 4*A001018(n). - R. J. Mathar, May 21 2024

E.g.f.: 4*exp(8*x). - Stefano Spezia, May 29 2024