cp's OEIS Frontend

A135690 a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.

%I A135690 #32 Nov 28 2021 04:43:37
%S A135690 0,1,-1,2,-4,-2,-6,0,-12,-8,-16,-4,-28,-20,-36,-12,-60,-44,-76,-28,
%T A135690 -124,-92,-156,-60,-252,-188,-316,-124,-508,-380,-636,-252,-1020,-764,
%U A135690 -1276,-508,-2044,-1532,-2556,-1020,-4092,-3068,-5116,-2044,-8188,-6140,-10236,-4092,-16380,-12284,-20476
%N A135690 a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.
%H A135690 G. C. Greubel, <a href="/A135690/b135690.txt">Table of n, a(n) for n = 0..1000</a>
%H A135690 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2).
%F A135690 G.f.: x*(1-2*x)*(1+3*x^2)/((1-x)*(1-2*x^4)). - _Colin Barker_, Jan 26 2013
%F A135690 a(n) = 4 - C*2^floor(n/4), where C = 4,3,5,2 according as n mod 4 = 0,1,2,3 respectively. - _Kevin Ryde_, Nov 26 2021
%t A135690 a[0] = 0; a[1] = 1; a[2] = -1; a[3] = 2; a[n_]:= a[n]= If[Mod[n, 2]==0, a[n-2] - (a[n-1] -a[n-2]), a[n-1] -(a[n-3] -a[n-4])]; Table[a[n], {n, 0, 60}]
%o A135690 (Sage)
%o A135690 @CachedFunction
%o A135690 def A135690(n):
%o A135690     if (n<2): return n
%o A135690     elif (n<4): return (-1)^(n+1)*(n-1)
%o A135690     elif (n%2==0): return A135690(n-2) - (A135690(n-1) - A135690(n-2))
%o A135690     else: return A135690(n-1) - (A135690(n-3) - A135690(n-4))
%o A135690 [A135690(n) for n in (0..60)] # _G. C. Greubel_, Nov 24 2021
%o A135690 (PARI) a(n) = 4 - [4,3,5,2][n%4+1] << (n>>2); \\ _Kevin Ryde_, Nov 26 2021
%Y A135690 Cf. A135689, A135692.
%K A135690 easy,sign,less
%O A135690 0,4
%A A135690 _Roger L. Bagula_, Feb 19 2008
%E A135690 Edited by _G. C. Greubel_ and _Kevin Ryde_, Nov 24 2021