A177101 The number of cycles in the Vers de Verres game, where 'worms' are transferred between 'cups' in a deterministic fashion. Because this defines a finite-state automaton, we know that every state eventually enters a cycle (or fixed point, which is essentially a cycle of length 1). The number of 'cups' (frequently called 'n') is a parameter for this automaton, and so we count the cycles (and fixed points) with respect to n.

1, 2, 4, 7, 13, 14, 20

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

Table of n, a(n) for n=1..7.

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

Related to A151986, A151987, A176336.

Sequence in context: A280028 A094271 A194422 * A018414 A002152 A163522

Adjacent sequences: A177098 A177099 A177100 * A177102 A177103 A177104

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