A132951 Period 6: repeat [1, 3, 1, -1, -3, -1].

1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1

Offset: 0

Author

Paul Curtz, Nov 22 2007

Keywords

• sign
• easy
• less

Links

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

Crossrefs

Cf. A109007, A130151, A131531.

Programs

Magma

&cat [[1, 3, 1, -1, -3, -1]: n in [0..20]]; // Wesley Ivan Hurt, Nov 18 2022

Mathematica

PadRight[{},120,{1,3,1,-1,-3,-1}] (* Harvey P. Dale, Feb 26 2024 *)

PARI

a(n)=[1,3,1,-1,-3,-1][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

a(n) = 3*a(n-1)-a(n-3)+3*a(n-4).

O.g.f.: (1+3*x+x^2)/((x+1)*(x^2-x+1)) = -(1/3)/(x+1)+(1/3)*(4*x+4)/(x^2-x+1). - R. J. Mathar, Nov 28 2007

a(n) = -(1/3)*(-1)^n+(4/3)*cos(Pi*n/3)+(4*3^0.5/3)*sin(Pi*n/3). - Richard Choulet, Jan 02 2008

a(n) = a(n-6) = A131531(n+3)+A131531(n+1)+3*A131531(n+2). - R. J. Mathar, Apr 04 2008

a(n) = A109007(n+2) * A130151(n). - Wesley Ivan Hurt, Jun 22 2013

Extensions

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar.