A105398 A simple "Fractal Jump Sequence" (FJS).

4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4

Offset: 4

Author

Eric Angelini, May 01 2005

Keywords

• nonn
• base
• easy

Comments

See A105397 for definition of Fractal Jump Sequence.

Continued fraction expansion of (4+3*sqrt(2))/2. - Bruno Berselli, Nov 09 2011

Period 2: repeat [4, 8]. - Wesley Ivan Hurt, Feb 12 2017

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A105397.

Programs

Maple

A105398:=n->2*(3-(-1)^n): seq(A105398(n), n=0..150); # Wesley Ivan Hurt, Feb 12 2017

Mathematica

PadRight[{}, 110, {4,8}] (* Harvey P. Dale, Nov 09 2011 *)

Maxima

makelist(if evenp(n) then 4 else 8, n, 0, 30); /* Martin Ettl, Nov 12 2012 */

Sage

[power_mod(2,n,12)for n in range(2,108)] # Zerinvary Lajos, Nov 03 2009

Formula

G.f.: -4*x^4*(1+2*x) / ( (x-1)*(1+x) ). - R. J. Mathar, Jul 07 2011

a(n) = a(-n) = a(n-2) = 2*(3-(-1)^n) = 2^((5-(-1)^n)/2). - Bruno Berselli, Nov 09 2011