A360362 Maximum number of moves required to reach an already visited color configuration, when applying the move described in A360360 to a deck of n colored cards.

1, 2, 3, 6, 9, 13, 20, 30, 46, 74, 106, 152, 242, 318

Offset: 1

Author

Pontus von Brömssen, Feb 04 2023

Keywords

• nonn
• more

Examples

			For n = 5, the initial configuration 01102 (with the top of the deck to the left) requires 9 moves to reach an already visited configuration: 01102 -> 11020 -> 10120 -> 01210 -> 12100 -> 21010 -> 12010 -> 20101 -> 02101 -> 21010. This is the maximum for 5 cards, so a(5) = 9.
Lexicographically first optimal initial configuration for 1 <= n <= 14:
   n  a(n)  configuration
   1    1   0
   2    2   01
   3    3   001
   4    6   0012
   5    9   01102
   6   13   010012
   7   20   0111023
   8   30   01232213
   9   46   012110234
  10   74   0111234234
  11  106   01112343324
  12  152   011102345345
  13  242   0122112345345
  14  318   01112345326546
		

Crossrefs

Cf. A357619, A360360, A360361.

Formula

a(n) = A357619(n) for 1 <= n <= 8, but it seems unlikely that this holds for all n.

a(n) <= A360360(n) + A360361(n). Equality holds (i.e., the maximum period and the maximum preperiod can be obtained with the same initial configuration) for n = 1, 2, 3, 4, 10, 12, 14, ... .