A152892 Period 5: repeat [0, 3, 1, 0, 1].

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

Offset

0,2

Links

Table of n, a(n) for n=0..104.

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

Formula

a(n+5) = a(n) with a(0) = a(3) = 0, a(1) = 3 and a(2) = a(4) = 1.

O.g.f: ((3*z+z^2+z^4)/(1-z^5)).

a(n) = 1 + (-1/2 + (3/10)*sqrt(5))*cos(2*n*Pi/5) + ((1/5)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/10)*sqrt(2)*sqrt(5 - sqrt(5)))*sin(2*n*Pi/5) + (-1/2 - (3/10)*sqrt(5))*cos(4*n*Pi/5) + (-(1/10)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/5)*sqrt(2)*sqrt(5-sqrt(5)))*sin(4*n*Pi/5).

a(n) = (n^3 + 2*n^2) mod 5. - Gary Detlefs, Mar 20 2010

Maple

seq((n^3+2*n^2)mod 5, n=0..50); # Gary Detlefs, Mar 20 2010

Mathematica

PadRight[{}, 120, {0, 3, 1, 0, 1}] (* Harvey P. Dale, Oct 04 2016 *)

Crossrefs

Cf. A026053, A026068.

Sequence in context: A245756 A360672 A322512 * A193002 A366725 A122960

Adjacent sequences: A152889 A152890 A152891 * A152893 A152894 A152895

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved