A072851 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)).

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, 1, 120, 579, 432, 675, 1320, 1325, 291, 259, 3332, 3657, 3724, 6015, 11114, 6465, 4325, 20433, 28884, 381, 5813, 91505, 96956, 70329, 106037, 260323, 260690, 78399

Offset: 0

Author

Roger L. Bagula, Jul 25 2002

Keywords

• nonn

Comments

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

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).

References

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

Programs

Mathematica

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

Extensions

Edited and extended by Robert G. Wilson v, Jul 29 2002

Name clarified by Sean A. Irvine, Nov 01 2024