%I #44 Oct 30 2025 11:22:13

%S 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,

%T 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,

%U 1,2,4,8,1,2,4,8,1,2,4,8

%N Period 4: repeat [1, 2, 4, 8].

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

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

%F a(n) = 2^(n mod 4). - _Jaume Oliver Lafont_, Mar 27 2009

%F a(n) = A160700(A000079(n)). - _Reinhard Zumkeller_, Jun 10 2009

%F From _R. J. Mathar_, Apr 13 2010: (Start)

%F a(n) = 2^n (mod 15).

%F G.f.: (1+2*x)*(4*x^2+1)/ ((1-x)*(1+x)*(x^2+1)). (End)

%F From _Wesley Ivan Hurt_, Jul 09 2016: (Start)

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

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

%F E.g.f.: 5*cosh(x)/2 - 3*(cos(x) + 2*sin(x))/2 + 5*sinh(x). - _Stefano Spezia_, Oct 30 2025

%p seq(op([1, 2, 4, 8]), n=0..50); # _Wesley Ivan Hurt_, Jul 09 2016

%t PadRight[{}, 100, {1, 2, 4, 8}] (* _Wesley Ivan Hurt_, Jul 09 2016 *)

%t Table[First@ IntegerDigits[2^n, 16], {n, 0, 120}] (* _Michael De Vlieger_, Jul 09 2016 *)

%o (PARI) a(n)=2^(n%4) \\ _Jaume Oliver Lafont_, Mar 27 2009

%o (SageMath) [power_mod(2,n,15) for n in range(0,80)] # _Zerinvary Lajos_, Nov 03 2009

%o (Magma) &cat [[1, 2, 4, 8]^^30]; // _Wesley Ivan Hurt_, Jul 09 2016

%Y Cf. A069705.

%Y Cf. A000079, A160700.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Dec 16 2007