A135169 - OEIS

%I #23 Feb 27 2024 03:02:31

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

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

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).

%F From _R. J. Mathar_, Feb 19 2008: (Start)

%F G.f.: -4/(x^2+1) - 5/(x-1).

%F a(n) = 5 - 4*A056594(n).

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

%F From _Wesley Ivan Hurt_, Jul 08 2016: (Start)

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

%F a(n) = 5 - 4*cos(n*Pi/2). (End)

%F E.g.f.: 5*exp(x) - 4*cos(x). - _G. C. Greubel_, Sep 30 2016

%p seq(op([1, 5, 9, 5]), n=0..50); # _Wesley Ivan Hurt_, Jul 08 2016

%t PadRight[{}, 100, {1, 5, 9, 5}] (* _Wesley Ivan Hurt_, Jul 08 2016 *)

%o (Magma) &cat [[1, 5, 9, 5]^^30]; // _Wesley Ivan Hurt_, Jul 08 2016

%o (PARI) a(n)=([0,1,0; 0,0,1; 1,-1,1]^n*[1;5;9])[1,1] \\ _Charles R Greathouse IV_, Sep 30 2016

%Y Cf. A056594.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Feb 14 2008