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A013731 a(n) = 2^(3*n+2). 7
4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936, 576460752303423488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Agrees with the independence number of the (n+1)-Sierpinski carpet graph for at least 1 <= n <= 5. - Eric W. Weisstein, Sep 06 2017

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, 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).

FORMULA

a(n) = 8*a(n-1), n>0 ; a(0)=4. G.f.: 4/(1-8x). - Philippe Deléham, Nov 23 2008

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

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

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 *)

PROG

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

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

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

CROSSREFS

Cf. A013730.

Cf. A092811 (same sequence with 1 prepended).

Sequence in context: A108449 A213413 A092811 * A009509 A036725 A065089

Adjacent sequences:  A013728 A013729 A013730 * A013732 A013733 A013734

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 21 19:00 EDT 2017. Contains 293698 sequences.