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%I #26 Sep 08 2022 08:45:51
%S 0,4,1,4,1,4,1,4,2,4,1,4,3,4,1,4,4,4,1,4,5,4,1,4,6,4,1,4,7,4,1,4,8,4,
%T 1,4,9,4,1,4,10,4,1,4,11,4,1,4,12,4,1,4,13,4,1,4,14,4,1,4,15,4,1,4,16,
%U 4,1,4,17,4,1,4,18,4,1,4,19,4,1,4,20,4,1,4
%N a(4n)=n, a(4n+1)=4, a(4n+2)=1, a(4n+3)=4.
%H Antti Karttunen, <a href="/A174571/b174571.txt">Table of n, a(n) for n = 0..16383</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F a(n) = A010685(n) if 4 does not divide n.
%F a(n) = 2*a(n-4) - a(n-8).
%F G.f.: x*(4 + x + 4*x^2 + x^3 - 4*x^4 - x^5 - 4*x^6)/( (1-x)*(1+x)*(1+x^2) )^2.
%F a(n) = (36 +n +(n-28)*(-1)^n +2*(n -5 +(-1)^n)*cos(n*Pi/2) +(1+(-1)^n)*sin(n*Pi/2) )/16. - _Wesley Ivan Hurt_, May 07 2021
%F E.g.f.: (1/8)*(4*cosh(x) + (x+32)*sinh(x) - 4*cos(x) - x*sin(x)). - _G. C. Greubel_, Nov 23 2021
%t Array[Which[OddQ@ Mod[#, 4], 4, Mod[#, 4] == 0, #/4, True, 1] &, 84, 0] (* or *)
%t CoefficientList[Series[x*(4 +x +4*x^2 +x^3 -4*x^4 -x^5 -4*x^6)/(1-x^4)^2, {x, 0, 83}], x] (* _Michael De Vlieger_, Nov 06 2018 *)
%o (PARI) A174571(n) = if(!(n%4),n/4,if(2==(n%4),1,4)); \\ _Antti Karttunen_, Nov 06 2018
%o (Magma) [(n mod 4) eq 0 select n/4 else Modexp(4,n,5): n in [0..90]]; // _G. C. Greubel_, Nov 23 2021
%o (Sage)
%o def A174571(n): return n/4 if (n%4==0) else power_mod(4,n,5)
%o [A174571(n) for n in (0..90)] # _G. C. Greubel_, Nov 23 2021
%Y Cf. A010685.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Nov 29 2010
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