%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