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%I #33 Dec 12 2021 02:24:11
%S 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 32,52,64,56,24,40,32,64,-32,-72,-24,-16,-8,-72,-16,-8,-48,-32,-104,
%U -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 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 G. C. Greubel, <a href="/A135692/b135692.txt">Table of n, a(n) for n = 0..1000</a>
%H Kevin Ryde, <a href="/A135692/a135692.gp.txt">PARI/GP Code and Notes</a>
%F 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 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 Table[a[n], {n, 0, 80}]
%o (Sage)
%o @CachedFunction
%o def A135692(n):
%o if (n<2): return n
%o elif (n<4): return -2^(n-1)
%o elif (n%2==0): return A135692(n-2) - 2*(A135692(n//2) - A135692(abs(n//2 -1)))
%o else: return A135692(n-1) - 2*(A135692(abs(n//2 -2)) - A135692(abs(n//2 -3)))
%o [A135692(n) for n in (0..80)] # _G. C. Greubel_, Nov 24 2021
%o (PARI) See links.
%Y Cf. A135689, A135690.
%K sign,easy
%O 0,3
%A _Roger L. Bagula_, Feb 21 2008
%E Edited by _G. C. Greubel_, Nov 24 2021
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