A228950 The index of Simon's piecewise testability congruence, for words of length n over a 2-letter alphabet.

1, 4, 16, 68, 312, 1560, 8528, 50864, 329248, 2298592, 17203264, 137289920

Offset

0,2

Comments

Consider an alphabet with two letters, say {0,1}. For two words v and w over this alphabet, we say v embeds in w, or v is a subsequence of w, if v can be obtained from w by erasing some (occurrences of) letters.

For a natural number n, define two words to be n-equivalent if they have the same subsequences of length up to n. The n-th term of this sequence is the number of equivalence classes of this equivalence relation.

Links

Table of n, a(n) for n=0..11.

Prateek Karandikar and Philippe Schnoebelen, On the index of Simon's congruence for piecewise testability, arXiv:1310.1278 [cs.FL], 2013-2014.

Example

For n=1, here are representatives of each of the four equivalence classes (taking the alphabet to be {0,1}) : empty word, 0, 1, 01.

Crossrefs

Sequence in context: A006319 A202020 A059606 * A354121 A297203 A231297

Adjacent sequences: A228947 A228948 A228949 * A228951 A228952 A228953

Keyword

nonn,more

Author

Prateek Karandikar and Philippe Schnoebelen, Oct 09 2013

Status

approved