A101000 Periodic sequence with period 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

0,3

Links

Table of n, a(n) for n=0..98.

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A014513 A144388 A133513 * A035653 A126595 A286096

Adjacent sequences: A100997 A100998 A100999 * A101001 A101002 A101003

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 17 2007

Status

approved