A174630 A weight function for the case N = 24 and k = 6 in Butler-Graham shuffling.

0, 1, 4, 5, 6, 7, 1, 2, 5, 6, 7, 8, 1, 2, 3, 4, 7, 8, 2, 3, 4, 5, 8, 9

Offset

0,3

Comments

Example from p.12 of Butler. Abstract: We consider a problem of shuffling a deck of cards with ordered labels. Namely we split the deck of N=k^tq cards (where t>=1 is maximal) into k equally sized stacks and then take the top card off of each stack and sort them by the order of their labels and add them to the shuffled stack. We show how to find stacks of cards invariant and periodic under the shuffling. We also show when gcd(q,k)=1 the possible periods of this shuffling are all divisors of order_k(N-q).

Links

Table of n, a(n) for n=0..23.

Steve Butler, R. L. Graham, Shuffling with ordered cards, March 23, 2010.

Crossrefs

Sequence in context: A046345 A325103 A004445 * A163875 A244586 A334501

Adjacent sequences: A174627 A174628 A174629 * A174631 A174632 A174633

Keyword

nonn,fini,full

Author

Jonathan Vos Post, Mar 24 2010

Status

approved