A135564 - OEIS

%I #26 Nov 29 2021 03:56:38

%S 0,1,3,-1,-2,-3,4,2,1,0,1,7,-7,-10,2,2,1,-7,1,10,-1,-2,-6,-6,14,12,3,

%T -2,-12,8,0,-11,1,-14,8,20,-8,-7,-9,-2,11,-5,1,0,4,24,0,-10,-20,-17,2,

%U -2,9,-11,5,27,10,17,-20,-24,8,13,11,-19,-12,16,15,18,-22,-45,-12,15,28,-9,-1,9,2,42,-7,-36,-13,-10,16,7,-6,-12,1,30,-4

%N a(n) defined by a(2*n) = a(2*n-2) - (a(n) - 2*a(n-1) + a(n-2)) for n > 2, a(2*n+1) = a(2*n) - (a(n-2) - 2*a(n-3) + a(n-4)), for n > 3, with a(0)=0, a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=-3, a(6)=4, a(7)=2.

%H G. C. Greubel, <a href="/A135564/b135564.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(2*n) = a(2*n-2) - (a(n) - 2*a(n-1) + a(n-2)), for n > 2.

%F a(2*n+1) = a(2*n) - (a(n-2) - 2*a(n-3) + a(n-4)), for n > 3.

%t a[0]:=0; a[1]:=1; a[2]:=3; a[3]:=-1; a[4]:=-2; a[5]:=-3; a[6]:=4; a[7]:=2;

%t a[n_]:= a[n]= If[Mod[n, 2]==0, a[n-2] -a[n/2] +2*a[n/2 -1] -a[n/2 -2], a[n-1] -a[(n-1)/2 -2] +2*a[(n-1)/2 -3] -a[(n-1)/2 -4]];

%t Table[a[n], {n, 0, 100}]

%o (Sage)

%o @CachedFunction

%o def a(n): # A135564

%o     if (n<8): return [0, 1, 3, -1, -2, -3, 4, 2][n]

%o     elif ((n%2)==0): return a(n-2) - a(n/2) + 2*a(n/2 - 1) - a(n/2 -2)

%o     else: return a(n-1) - a((n-1)/2 - 2) + 2*a((n-1)/2 - 3) - a((n-1)/2 -4)

%o [a(n) for n in (0..100)] # _G. C. Greubel_, Nov 26 2021

%Y Cf. A122581, A135689, A135690, A135692.

%K sign,easy,less

%O 0,3

%A _Roger L. Bagula_, Feb 23 2008

%E Edited by _G. C. Greubel_, Nov 28 2021