A175922 Period 5: repeat [1, 1, 2, -1, 2].

1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2, 1, 1, 2, -1, 2

Offset: 1

Author

Jaroslav Krizek, Oct 17 2010

Keywords

• sign
• easy
• less

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Crossrefs

Cf. A040001, A028356, A142150, A000012, A175921.

Programs

GAP

Flat(List([1..30],n->[1,1,2,-1,2])); # Muniru A Asiru, Sep 28 2018

Magma

&cat[[1, 1, 2, -1, 2]^^20]; // Vincenzo Librandi, Sep 28 2018

Maple

seq(op([1,1,2,-1,2]),n=1..30); # Muniru A Asiru, Sep 28 2018

Mathematica

PadRight[{}, 100, {1, 1, 2, -1, 2}] (* Vincenzo Librandi, Sep 28 2018 *)

PARI

a(n)=[2,1,1,2,-1][n%5+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = 1 + (2/5)*(cos(2*n*Pi/5) + cos(4*n*Pi/5) - 2*cos(2*(n+1)*Pi/5) - sin((4*n+3)*Pi/10) + 2*sin((8*n+3)*Pi/10) + sin((8*n+1)*Pi/10)). - Wesley Ivan Hurt, Sep 27 2018

G.f.: x*(1 + x + 2*x^2 - x^3 + 2*x^4) / (1 - x^5). - Vincenzo Librandi, Sep 28 2018

a(n) = a(n-5). - Wesley Ivan Hurt, Jun 25 2022

Extensions

Edited by Joerg Arndt, Sep 16 2013