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
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 entries for linear recurrences with constant coefficients, signature (8).
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
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 range(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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved