

A065240


Number of winning length n strings with a 7symbol alphabet in "same game".


11



1, 0, 7, 7, 91, 217, 1561, 5593, 32011, 139363, 732697, 3492265, 17899609, 89014933, 455041825, 2311847083, 11875575355, 61080825757
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OFFSET

0,3


COMMENTS

Strings that can be reduced to null string by repeatedly removing an entire run of two or more consecutive symbols.
For binary strings, the formula for the number of winning strings of length n has been conjectured by Ralf Stephan and proved by Burns and Purcell (2005, 2007). For bary strings with b >= 3, the same problem seems to be unsolved.  Petros Hadjicostas, Aug 31 2019


LINKS

Table of n, a(n) for n=0..17.
Chris Burns and Benjamin Purcell, A note on Stephan's conjecture 77, preprint, 2005. [Cached copy]
Chris Burns and Benjamin Purcell, Counting the number of winning strings in the 1dimensional same game, Fibonacci Quarterly, 45(3) (2007), 233238.
Sascha Kurz, Polynomials in "same game", 2001. [ps file]
Sascha Kurz, Polynomials for same game, 2001. [pdf file]
Ralf Stephan, Prove or disprove: 100 conjectures from the OEIS, arXiv:math/0409509 [math.CO], 2004.


EXAMPLE

11011001 is a winning string since 110{11}001 > 11{000}1 > {111} > null.


CROSSREFS

Cf. A035615, A035617, A065237, A065238, A065239, A065241, A065242, A065243, A309874, A323812.
Row b=7 of A323844.
Sequence in context: A219353 A269902 A269937 * A178708 A072399 A001988
Adjacent sequences: A065237 A065238 A065239 * A065241 A065242 A065243


KEYWORD

nonn,more


AUTHOR

Sascha Kurz, Oct 23 2001


EXTENSIONS

a(12)a(17) from Bert Dobbelaere, Dec 26 2018


STATUS

approved



