OFFSET
1,2
COMMENTS
The game is described in the websites listed, and already has other sequences, e.g., A151986. Note that this also gives the number of connected components, if we draw a graph of this process. The sequence gives the number of cycles, for a given number of cups. The sequence is increasing (append a 0 to all configurations in a cycle, and you get the same cycle with one more cup). It is strictly increasing since {n-1,0,0,0...,0} occurs in a cycle at stage n, but never before.
I am not clear on how this is meant to differ from A176450; my calculations reproduce the terms there not the ones in this sequence. - Joseph Myers, Nov 13 2010
LINKS
Eric Angelini - Vers de Verres
E. Angelini, Vers de verres (Glass worms) [Cached copy, with permission]
Kellen Myers - Vers de Verres [Broken link]
EXAMPLE
For n=4, there are seven cycles: {0300,3000,0030}, {3300,3003,0330}, {0200,2000}, {3330}, {2200}, {1000}, {0000}. Note that four of these are "inherited" from n=3, as described above.
CROSSREFS
KEYWORD
more,nonn,obsc,uned
AUTHOR
Kellen Myers, May 02 2010
EXTENSIONS
Fixed error in sequence. Added small amount of formatting changes and elaboration. - Kellen Myers, May 03 2010
STATUS
approved