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

0,9

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.

Links

Table of n, a(n) for n=0..55.

Mathematica

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}]

Crossrefs

Sequence in context: A265146 A358136 A325537 * A246688 A103627 A344088

Adjacent sequences: A072848 A072849 A072850 * A072852 A072853 A072854

Keyword

nonn

Author

Roger L. Bagula, Jul 25 2002

Extensions

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

Name clarified by Sean A. Irvine, Nov 01 2024

Status

approved