A101000 Period 3: repeat [0, 1, 3].

0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3, 0, 1, 3

Offset: 0

Author

N. J. A. Sloane, Jun 17 2007

Keywords

• nonn
• easy

Links

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

Programs

Maple

A101000:=n->2^(n mod 3) - 1; seq(A101000(n), n=0..100); # Wesley Ivan Hurt, Apr 16 2014

Mathematica

PadRight[{},120,{0,1,3}] (* Harvey P. Dale, Apr 28 2012 *)
Table[2^Mod[n, 3] - 1, {n, 0, 100}] (* Wesley Ivan Hurt, Apr 16 2014 *)

PARI

a(n)=n%3+(n%3==2) \\ Jaume Oliver Lafont, Mar 24 2009

PARI

a(n)=2^(n%3)-1 \\ Jaume Oliver Lafont, Mar 24 2009

Formula

a(n) = floor((n mod 3)*3/2). - Reinhard Zumkeller, Jun 23 2007

a(n) = 4 - a(n-1) - a(n-2) for n > 1. - Reinhard Zumkeller, Apr 13 2008

G.f.: x*(1+3*x)/(1-x^3). - Jaume Oliver Lafont, Mar 24 2009

a(n) = 2^(n mod 3) - 1. - Wesley Ivan Hurt, Apr 16 2014

a(n) = (7*a(n-1) + 2)*(3 - a(n-1))/6 for n > 0. - Nicolas Bělohoubek, Oct 09 2024