A165207 Period 4: repeat [2, 2, 4, 4].

2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2

Offset: 0

Author

Paul Curtz, Sep 07 2009

Keywords

• nonn
• easy

Comments

Continued fraction expansion of (21+5*sqrt(26))/19 = A177153. - Klaus Brockhaus, May 03 2010

A045572(n)^a(n) == 1 (mod 10). For n>1, a(n) is the smallest positive exponent with this property. - Christina Steffan, Sep 08 2015

Links

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

Crossrefs

Cf. A002378, A045572, A061037, A061041, A064038, A130658, A177153.

Programs

Magma

&cat[[2,2,4,4]^^30]; // Vincenzo Librandi, Feb 08 2016

Maple

seq(op([2, 2, 4, 4]), n=0..50); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

PadRight[{}, 120, {2,2,4,4}] (* Harvey P. Dale, Oct 08 2014 *)

PARI

a(n)=n\2*2%4 + 2 \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = 2*A130658(n).

a(n) = A002378(n+1)/A064038(n+2) = A061037(4n+6)/A064038(n+2) = A061037(4n+6)/A061041(8n+12).

From R. J. Mathar, Sep 11 2009: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.

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

a(n) = 3-cos(Pi*n/2)-sin(Pi*n/2). - R. J. Mathar, Oct 08 2011

a(n) = 2 + (2*floor(n/2) mod 4). - Wesley Ivan Hurt, Apr 20 2015

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

Extensions

Edited, offset set to 0, by R. J. Mathar, Sep 11 2009