A360361
Maximum length of the transient part when repeatedly applying the move described in A360360 to a deck of n colored cards.
Original entry on oeis.org
0, 0, 1, 4, 6, 11, 18, 24, 44, 58, 96, 120, 210, 254
Offset: 1
For n = 5, the initial configuration 01112 (with the top of the deck to the left) requires 6 moves to reach the first configuration in the eventual cycle: 01112 -> 10112 -> 01121 -> 10121 -> 01211 -> 10211 -> 02111 -> 20111 -> 02111. This is the maximum for 5 cards, so a(5) = 6.
Lexicographically first optimal initial configuration for 1 <= n <= 14:
n a(n) configuration
1 0 0
2 0 00
3 1 001
4 4 0012
5 6 01112
6 11 011023
7 18 0111023
8 24 01221034
9 44 012110234
10 58 0111234234
11 96 01200321345
12 120 011102345345
13 210 0122112345345
14 254 01112345326546
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.
Original entry on oeis.org
1, 2, 3, 6, 9, 13, 20, 30, 46, 74, 106, 152, 242, 318
Offset: 1
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
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