A173469 Number of permutations of length n that can be sorted in 2^(n-1)-1 steps of Elizalde and Winkler's homing algorithm

1, 2, 5, 16, 62, 280, 1440, 8296, 52864, 368848, 2794864, 22842048, 200201408, 1872466944, 18608903968, 195778297664, 2173272774016, 25380361760000, 311011886153856, 3989579297299712, 53458990592638976, 746817531317769728

Offset

2,2

Comments

The maximum number of steps that the homing algorithm can take to sort a permutation of length n is 2^(n-1)-1. This sequence counts permutations for which it is possible to use these many steps.

References

S. Elizalde and P. Winkler, Sorting by Placement and Shift, Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009.

Links

Table of n, a(n) for n=2..23.

S. Elizalde and P. Winkler, Sorting by placement and shift

Formula

a(n) is the coefficient of t^n in the generating function F(t,t), where F(u,v) satisfies the partial differential equation F(u,v)=u*v+u*v*D_u(f)+u*v*D_v(f)-u^2*v^2*D_u(D_v(f)).

Crossrefs

Sequence in context: A124531 A129578 A005387 * A138549 A210667 A144188

Adjacent sequences: A173466 A173467 A173468 * A173470 A173471 A173472

Keyword

nonn

Author

Sergi Elizalde, Feb 18 2010

Status

approved