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%I #23 Oct 28 2022 17:10:29
%S 0,0,1,1,0,2,1,1,2,0,3,1,2,2,1,3,0,4,1,3,2,2,3,1,4,0,5,1,4,2,3,3,2,4,
%T 1,5,0,6,1,5,2,4,3,3,4,2,5,1,6,0,7,1,6,2,5,3,4,4,3,5,2,6,1,7,0,8,1,7,
%U 2,6,3,5,4,4,5,3,6,2,7,1,8,0,9,1,8,2,7,3,6,4,5,5,4,6,3,7,2,8,1,9,0,10,1,9,2
%N a(1)=0, a(2)=0, a(3)=1; for n>3, a(n)=abs(a(n-1)-a(n-2)-a(n-3)).
%C Conjecture: a(n) = m/2 where m is the smallest even distance from n to a square. - _Ralf Stephan_, Sep 23 2013
%H Reinhard Zumkeller, <a href="/A088226/b088226.txt">Table of n, a(n) for n = 1..10000</a>
%F a(k^2+2m+2)=k-m and a(k^2+2m+1)= m, for k>=0 and 0<=m<=k.
%t RecurrenceTable[{a[1]==a[2]==0,a[3]==1,a[n]==Abs[a[n-1]-a[n-2]-a[n-3]]},a,{n,110}] (* _Harvey P. Dale_, Apr 13 2012 *)
%o (PARI) a(n)=t=sqrtint(n);if((n-t*t)%2==0,(n-t*t)/2,((t+1)^2-n)/2) // - _Ralf Stephan_, Sep 23 2013
%o (Haskell)
%o a088226 n = a088226_list !! (n-1)
%o a088226_list = 0 : 0 : 1 : zipWith3 (\u v w -> abs (w - v - u))
%o a088226_list (tail a088226_list) (drop 2 a088226_list)
%o -- _Reinhard Zumkeller_, Oct 11 2014
%Y Cf. A080096.
%Y Cf. A077623, A077653, A079623, A079624, A080096.
%K nonn
%O 1,6
%A _Benoit Cloitre_, Nov 04 2003
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