A158459 Period 4: repeat [0, 3, 2, 1].

0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2

Offset

0,2

Links

Table of n, a(n) for n=0..86.

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

Formula

G.f.: x*(x^2+2*x+3)/(1-x^4).

a(n) = A102370(n) (mod 4).

a(n) = 3/2-(-1)^n/2+sin(n*Pi/2)-cos(n*Pi/2). - Richard Choulet, Apr 07 2009

a(n) = -n (mod 4). - M. F. Hasler, Jan 13 2012; formula simplified by Arkadiusz Wesolowski, Jul 03 2012

a(n) = (3-(-1)^n-2*I^(n*(n+1)))/2. - Bruno Berselli, Jul 03 2012

a(n) = floor(107/3333*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 04 2013

a(n) = floor(19/85*4^(n+1)) mod 4. - Hieronymus Fischer, Jan 04 2013

a(n) = ((n+1) mod 4)+(-1)^((n+1) mod 4). - Wesley Ivan Hurt, May 18 2014

a(n) = 3*n mod 4. - Gary Detlefs, May 24 2014

a(n) = a(n-4) for n>3. - Wesley Ivan Hurt, Jul 09 2016

Maple

seq(op([0, 3, 2, 1]), n=0..50); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

Flatten@Table[{0, 3, 2, 1}, {22}] (* Arkadiusz Wesolowski, Jul 03 2012 *)

Prog

(PARI) A158459(n)=(-n)%4 \\ M. F. Hasler, Jan 13 2012
(Haskell)
a158459 = (`mod` 4) . negate
a158459_list = cycle [0, 3, 2, 1]  -- Reinhard Zumkeller, Feb 22 2013
(Magma) &cat [[0, 3, 2, 1]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Crossrefs

Cf. A010873, A102370.

Sequence in context: A359677 A215486 A083721 * A319666 A307333 A031251

Adjacent sequences: A158456 A158457 A158458 * A158460 A158461 A158462

Keyword

nonn,easy

Author

Philippe Deléham, Mar 19 2009

Extensions

Better definition from M. F. Hasler, Jan 13 2012

Status

approved