cp's OEIS Frontend

A135692 a(n) = a(n-2) - 2*( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2*( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

%I A135692 #34 Dec 19 2024 11:46:19
%S A135692 0,1,-2,-4,4,6,8,6,-8,-2,-12,-8,-16,-32,-12,-16,16,12,4,8,24,52,16,4,
%T A135692 32,52,64,56,24,40,32,64,-32,-72,-24,-16,-8,-72,-16,-8,-48,-32,-104,
%U A135692 -112,-32,-64,-8,-64,-64,8,-104,-80,-128,-184,-112,-152,-48,-72,-80,-64,-64,0,-128,-160,64,80,144,80,48,240,32,112,16,-80
%N A135692 a(n) = a(n-2) - 2*( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2*( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.
%H A135692 G. C. Greubel, <a href="/A135692/b135692.txt">Table of n, a(n) for n = 0..1000</a>
%H A135692 Kevin Ryde, <a href="/A135692/a135692.gp.txt">PARI/GP Code and Notes</a>
%F A135692 a(n) = a(n-2) - 2*( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2*( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.
%t A135692 a[n_]:= a[n]= If[n<2, n, If[n<4, -2^(n-1), If[Mod[n, 2]==0, a[n-2] - 2*( a[Floor[n/2]] - a[Abs[Floor[n/2] -1]]), a[n-1] - 2*(a[Abs[Floor[n/2] -2]] - a[Abs[Floor[n/2] -3]]) ]]];
%t A135692 Table[a[n], {n, 0, 80}]
%o A135692 (Sage)
%o A135692 @CachedFunction
%o A135692 def A135692(n):
%o A135692     if (n<2): return n
%o A135692     elif (n<4): return -2^(n-1)
%o A135692     elif (n%2==0): return A135692(n-2) - 2*(A135692(n//2) - A135692(abs(n//2 -1)))
%o A135692     else: return A135692(n-1) - 2*(A135692(abs(n//2 -2)) - A135692(abs(n//2 -3)))
%o A135692 [A135692(n) for n in (0..80)] # _G. C. Greubel_, Nov 24 2021
%o A135692 (PARI) \\ See links.
%Y A135692 Cf. A135689, A135690.
%K A135692 sign,easy
%O A135692 0,3
%A A135692 _Roger L. Bagula_, Feb 21 2008
%E A135692 Edited by _G. C. Greubel_, Nov 24 2021