login
Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4.
0

%I #26 Dec 12 2023 07:44:22

%S 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4,1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4,1,1,

%T 1,2,1,1,1,2,1,1,1,4,1,1,1,4,1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4,1,1,1,2,

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

%N Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4.

%C The numerator of the reduced fraction A061037(n+3)/A061041(2n+6).

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,-1,0,0,0,1).

%F a(n) = a(n-4) - a(n-8) + a(n-12). - _R. J. Mathar_, Dec 17 2010

%F G.f.: ( -1 - x - x^2 - 2*x^3 - x^8 - x^9 - x^10 - 4*x^11 ) / ( (x-1)*(1+x)*(1+x^2)*(x^8+1) ). - _R. J. Mathar_, Dec 17 2010

%F a(4n) = a(4n+1) = a(4n+2) = 1. a(4n+3) = A165207(n).

%t LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1}, {1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4}, 50] (* _G. C. Greubel_, Apr 20 2016 *)

%o (PARI) x='x+O('x^50); Vec(( -1-x-x^2-2*x^3-x^8-x^9-x^10-4*x^11 )/((x-1)*(1+x)*(1+x^2)*(x^8+1))) \\ _G. C. Greubel_, Sep 20 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(( -1-x-x^2-2*x^3-x^8-x^9-x^10-4*x^11 )/((x-1)*(1+x)*(1+x^2)*(x^8+1)))); // _G. C. Greubel_, Sep 20 2018

%Y Cf. A064038.

%K nonn,easy,less

%O 0,4

%A _Paul Curtz_, Oct 03 2009