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a(n) = s(2*n) where s(0) = 0, s(1) = s(2) = 1, s(n) = abs(Sum_{k=2..n-1} (-1)^k * s(n-k) * s(k)).
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%I #12 Nov 01 2024 18:10:12

%S 0,1,0,1,1,1,0,1,2,1,2,3,1,3,4,1,3,5,6,1,7,29,14,41,82,39,58,109,119,

%T 1,120,579,432,675,1320,1325,291,259,3332,3657,3724,6015,11114,6465,

%U 4325,20433,28884,381,5813,91505,96956,70329,106037,260323,260690,78399

%N a(n) = s(2*n) where s(0) = 0, s(1) = s(2) = 1, s(n) = abs(Sum_{k=2..n-1} (-1)^k * s(n-k) * s(k)).

%C Derived from G.J. Chaitin's s formula.

%C Chaitin's expression is s(0)=0, s(1)=alpha, s(2)=1, s(n)=Sum_{k=2..n-1} s(n-k)*s(k), but here it is made to alternate with the introduction of (-1)^k so that the numbers do not get large fast and alternate back and forth like a boustrophedon (A072231).

%D G.J. Chaitin, Algorithmic Information Theory, Cambridge Press, 1987, page 169.

%t s[n_Integer?Positive] := s[n]=Abs[Sum[(-1)^k*s[k-n]*s[k], {k, 2, n-1}]; s[0]=0; s[1]=1; s[2]=1; Table[ s[n], {n, 0, 200, 2}]

%K nonn,changed

%O 0,9

%A _Roger L. Bagula_, Jul 25 2002

%E Edited and extended by _Robert G. Wilson v_, Jul 29 2002

%E Name clarified by _Sean A. Irvine_, Nov 01 2024