|
| |
|
|
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.
|
|
2
|
|
|
|
1, 2, 3, 6, 9, 13, 20, 30, 46, 74, 106, 152, 242, 318
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
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, ... .
|
|
|
EXAMPLE
|
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
|
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
