A191247 First element in permutations in cool-lex ordering.

0, 1, 2, 0, 2, 1, 3, 1, 0, 1, 3, 0, 3, 1, 2, 3, 2, 0, 2, 3, 0, 3, 2, 1, 4, 1, 2, 4, 2, 1, 0, 1, 2, 0, 2, 1, 4, 1, 0, 1, 4, 0, 4, 1, 2, 4, 2, 0, 2, 4, 0, 4, 2, 1, 3, 1, 4, 1, 3, 4, 3, 1, 0, 1, 3, 0, 3, 1, 4, 1, 0, 1, 4, 0, 4, 1, 3, 4, 3, 0, 3, 4, 0, 4, 3, 1, 2, 3, 2, 4, 2, 3, 4, 3, 2, 0, 2, 3, 0, 3, 2, 4, 2, 0, 2, 4, 0, 4, 2, 3, 4, 3, 0, 3, 4, 0, 4, 3, 2, 1, 5, 1

Offset

0,3

Comments

Start with the identical permutation [0,1,2,...,n-1] and obtain the next permutation by finding the element a(n) (n>=1) and cyclically shifting the prefix ending in a(n) by one position to the right (see right column in example for A191246).

References

Aaron Williams, Loopless Generation of Multiset Permutations using a Constant Number of Variables by Prefix Shifts, ACM-SIAM Symposium on Discrete Algorithms (SODA09), (2009), see link.

Links

Table of n, a(n) for n=0..121.

SODA 2009 proceedings with Williams' paper: SIAM: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms.

Example

(see A191246).

Crossrefs

A191246 (size of shifted prefixes).

Sequence in context: A078152 A339242 A339222 * A308263 A028932 A076473

Adjacent sequences: A191244 A191245 A191246 * A191248 A191249 A191250

Keyword

nonn

Author

Joerg Arndt, May 28 2011

Status

approved