%I #8 Mar 13 2014 15:22:18
%S 0,0,0,1,1,1,0,0,0,-1,1,3,0,6,8,1,9,9,0,8,8,-1,9,11,0,14,16,1,17,17,0,
%T 16,16,-1,17,19,0,22,24,1,25,25,0,24,24,-1,25,27,0,30,32,1,33,33,0,32,
%U 32,-1,33,35,0,38,40,1,41,41,0,40,40,-1,41,43,0,46,48,1,49,49,0,48,48,-1,49,51,0,54,56,1,57,57,0,56,56,-1,57,59,0,62,64
%N a(1)=0, a(2)=0, a(3)=0, a(4)=1 then a(n)=abs(a(n-1)-2*a(n-2)+a(n-3))-a(n-4).
%D B. Cloitre, On strange predictible recursions, preprint 2006
%F for n>=1 : a(6*n)=4*n-4-(-1)^n, a(6n+1)=0, a(6*n+2)=4*n-3+(-1)^n, a(6*n+3)=4*n-2+2*(-1)^n, a(6*n+4)=(-1)^n, a(6*n+5)=4*n-1+2*(-1)^n.
%F Empirical g.f.: x^4*(2*x^10+5*x^8+3*x^7+x^6-2*x^5-2*x^4-2*x^3+x^2+x+1) / (x^12-2*x^9+2*x^6-2*x^3+1). - _Colin Barker_, Jun 28 2013
%t RecurrenceTable[{a[1]==a[2]==a[3]==0, a[4]==1,a[n]==Abs[a[n-1]-2a[n-2]+ a[n-3]]- a[n-4]},a,{n,100}] (* _Harvey P. Dale_, Mar 13 2014 *)
%Y Cf. A104156, A119557, A119558.
%K sign
%O 1,12
%A _Benoit Cloitre_, May 31 2006