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A360360
Given a deck of colored cards, move the top card below the bottom-most card of the same color, with one other card between them. (If the top and bottom cards have the same color, the top card is moved to the bottom of the deck; if there is no other card of the same color, the top card is moved one step down in the deck.) a(n) is the maximum, over all initial color configurations of a deck of n cards, of the length of the eventual cycle when repeatedly applying this move.
2
1, 2, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64
OFFSET
1,2
COMMENTS
Cards of the same color are considered identical. There can be any number of different colors.
Apparently the lengths of all cycles (not just the longest) are powers of 2.
FORMULA
It appears that a(n) = 2^floor((n-1)/2) for n != 2.
EXAMPLE
For n = 7, the initial configuration 0120323 (with the top of the deck to the left) leads to a cycle of length 8: 0120323 -> 1203023 -> 2103023 -> 1030232 -> 0130232 -> 1302032 -> 3102032 -> 1020323 -> 0120323. This is the maximum for 7 cards, so a(7) = 8.
CROSSREFS
Sequence in context: A350457 A010238 A178799 * A089819 A059888 A299204
KEYWORD
nonn,more
AUTHOR
STATUS
approved