%I #27 Jan 01 2024 11:27:19
%S 0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,
%T 2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,
%U 0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0,1,2,5,0
%N a(n) = A000975(n) mod 10.
%C A000975(0), A000975(1), A000975(2), A000975(3) repeating.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F G.f.: x*(1 + 2*x + 5*x^2)/(1 - x^4).
%F E.g.f.: 2*exp(x) - exp(-x) - cos(x) - 2*sin(x).
%F a(n) = 2 - (-1)^n - cos(Pi*n/2) - 2*sin(Pi*n/2).
%F a(n+4) = a(n). - _G. C. Greubel_, Sep 26 2017
%F 2*a(n) = (n mod 2) + (n mod 4)^2. - _Bruno Berselli_, Oct 18 2018
%t CoefficientList[Series[x (1 + 2 x + 5 x^2)/(1 - x^4), {x, 0, 50}], x] (* _G. C. Greubel_, Sep 26 2017 *)
%t PadRight[{},120,{0,1,2,5}] (* _Harvey P. Dale_, Apr 30 2022 *)
%o (PARI) x='x+O('x^50); Vec(x*(1+2*x+5*x^2)/(1-x^4)) \\ _G. C. Greubel_, Sep 26 2017
%K nonn,easy
%O 0,3
%A _Paul Barry_, Dec 18 2003