%I #4 Feb 26 2023 20:09:07
%S 0,0,1,4,6,11,18,24,44,58,96,120,210,254
%N Maximum length of the transient part when repeatedly applying the move described in A360360 to a deck of n colored cards.
%e 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.
%e Lexicographically first optimal initial configuration for 1 <= n <= 14:
%e n a(n) configuration
%e 1 0 0
%e 2 0 00
%e 3 1 001
%e 4 4 0012
%e 5 6 01112
%e 6 11 011023
%e 7 18 0111023
%e 8 24 01221034
%e 9 44 012110234
%e 10 58 0111234234
%e 11 96 01200321345
%e 12 120 011102345345
%e 13 210 0122112345345
%e 14 254 01112345326546
%Y Cf. A360360, A360362.
%K nonn,more
%O 1,4
%A _Pontus von Brömssen_, Feb 04 2023