A070370 - OEIS

%I #42 Dec 14 2023 05:12:20

%S 1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,

%T 13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,

%U 5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1,5,9,13,1

%N a(n) = 5^n mod 16.

%C Period 4: repeat [1, 5, 9, 13].

%H G. C. Greubel, <a href="/A070370/b070370.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1). [_R. J. Mathar_, Apr 20 2010]

%F From _R. J. Mathar_, Apr 20 2010: (Start)

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

%F G.f.: ( 1+5*x+9*x^2+13*x^3 ) / ( (1-x)*(1+x)*(1+x^2) ). (End)

%F a(n) = 7-2*((1+I)*(-I)^n+(1-I)*I^n+(-1)^n). - _Bruno Berselli_, Feb 07 2011

%F E.g.f.: 5*cosh(x) + 9*sinh(x) - 4*cos(x) - 4*sin(x). - _G. C. Greubel_, Mar 05 2016

%F a(n) = A130909(A000351(n)). - _Michel Marcus_, Jul 06 2016

%p seq(op([1, 5, 9, 13]), n=0..50); # _Wesley Ivan Hurt_, Jul 06 2016

%t Table[Mod[5^n, 16], {n, 0, 100}] (* _G. C. Greubel_, Mar 05 2016 *)

%o (Sage) [power_mod(5,n,16)for n in range(0,93)] # _Zerinvary Lajos_, Nov 26 2009

%o (PARI) a(n) = lift(Mod(5, 16)^n); \\ _Michel Marcus_, Mar 05 2016

%o (Magma) &cat [[1, 5, 9, 13]^^30]; // _Wesley Ivan Hurt_, Jul 06 2016

%Y Cf. A000351, A130909.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 12 2002