%I #27 Dec 06 2022 07:58:57
%S 0,1,1,1,4,1,1,1,8,1,1,1,12,1,1,1,16,1,1,1,20,1,1,1,24,1,1,1,28,1,1,1,
%T 32,1,1,1,36,1,1,1,40,1,1,1,44,1,1,1,48,1,1,1,52,1,1,1,56,1,1,1,60,1,
%U 1,1,64,1,1,1,68,1,1,1,72,1,1,1,76,1,1,1,80,1,1,1,84,1,1,1,88,1,1,1,92,1,1,1
%N a(4n) = 4n, otherwise a(n) = 1.
%H Antti Karttunen, <a href="/A088440/b088440.txt">Table of n, a(n) for n = 0..65537</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) = 1+(n-1)*((1+(-1)^(n/2))*(1+(-1)^n))/4. - _Wesley Ivan Hurt_, May 07 2021
%F G.f.: x*(1 + x + x^2 + 4*x^3 - x^4 - x^5 - x^6)/(1-x^4)^2. - _Georg Fischer_, Nov 17 2022
%F E.g.f.: (1/2)*( cosh(x) + (x+2)*sinh(x) - cos(x) - x*sin(x) ). - _G. C. Greubel_, Dec 05 2022
%t Array[1 + (# - 1)*((1 + (-1)^(#/2))*(1 + (-1)^#))/4 &, 96, 0] (* _Michael De Vlieger_, May 07 2021 *)
%o (PARI) A088440(n) = if((n%4),1,n); \\ _Antti Karttunen_, Jul 03 2018
%o (Magma)
%o A088440:= func< n | n mod 4 eq 0 select n else 1>;
%o [A088440(n): n in [0..120]]; // _G. C. Greubel_, Dec 05 2022
%o (SageMath)
%o def A088440(n): return 1 if (n%4) else n
%o [A088440(n) for n in range(121)] # _G. C. Greubel_, Dec 05 2022
%Y Cf. A088140.
%K nonn,easy
%O 0,5
%A _Roger L. Bagula_, Nov 09 2003
%E Description corrected by _Antti Karttunen_, Jul 03 2018