A133145 Period 4: repeat [1, 2, 4, 8].

1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 4, 8

Offset: 0

Author

Paul Curtz, Dec 16 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A069705. [Jaume Oliver Lafont, Mar 27 2009]

Cf. A000079, A160700.

Programs

Magma

&cat [[1, 2, 4, 8]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Maple

seq(op([1, 2, 4, 8]), n=0..50); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

PadRight[{}, 100, {1, 2, 4, 8}] (* Wesley Ivan Hurt, Jul 09 2016 *)
Table[First@ IntegerDigits[2^n, 16], {n, 0, 120}] (* Michael De Vlieger, Jul 09 2016 *)

PARI

a(n)=2^(n%4) \\ Jaume Oliver Lafont, Mar 27 2009

Sage

[power_mod(2,n,15) for n in range(0,80)] # Zerinvary Lajos, Nov 03 2009

Formula

a(n) == 2*a(n-1) mod 15.

a(n) = 2^(n mod 4). - Jaume Oliver Lafont, Mar 27 2009

a(n) = A160700(A000079(n)). [Reinhard Zumkeller, Jun 10 2009]

a(n) = 2^n (mod 15). G.f.: (1+2*x)*(4*x^2+1)/ ((1-x)*(1+x)*(x^2+1)). [R. J. Mathar, Apr 13 2010]

From Wesley Ivan Hurt, Jul 09 2016: (Start)

a(n) = a(n-4) for n>3.

a(n) = (15-6*cos(n*Pi/2)-5*cos(n*Pi)-12*sin(n*Pi/2)-5*I*sin(n*Pi))/4. (End)