A130974 Period 6: repeat [1, 1, 1, 3, 3, 3].

1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1

Offset

0,4

Links

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

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

Formula

G.f.: (1+3*x^3)/((1-x)*(1+x)*(1-x+x^2)). - R. J. Mathar, Nov 15 2007

a(n) = 2 - (2/3)*cos((1/3)*Pi*n) - (2/3)*3^(1/2)*sin((1/3)*Pi*n) + (1/3)*(-1)^(1+n). - R. J. Mathar, Nov 15 2007

a(n) = 2 - (-1)^floor(n/3). - Bruno Berselli, Jul 09 2013

a(n) = a(n-1) - a(n-3) + a(n-4) for n > 3. - Wesley Ivan Hurt, Jun 20 2016

Maple

A130974:=n->[1, 1, 1, 3, 3, 3][(n mod 6)+1]: seq(A130974(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

Mathematica

PadRight[{}, 100, {1, 1, 1, 3, 3, 3}] (* Wesley Ivan Hurt, Jun 20 2016 *)

Prog

(Magma) &cat [[1, 1, 1, 3, 3, 3]^^30]; // Wesley Ivan Hurt, Jun 20 2016
(PARI) a(n) = [1, 1, 1, 3, 3, 3][n%6+1]; \\ Jinyuan Wang, Feb 26 2020

Crossrefs

Cf. A177957 (decimal expansion of (12+3*sqrt(35))/19). - Klaus Brockhaus, May 16 2010

Sequence in context: A353631 A353641 A131289 * A064353 A190906 A355586

Adjacent sequences: A130971 A130972 A130973 * A130975 A130976 A130977

Keyword

nonn,easy

Author

Paul Curtz, Sep 28 2007

Status

approved