A065241 - OEIS

%I #31 Sep 02 2019 02:03:01

%S 1,0,8,8,120,288,2360,8632,55224,249656,1443128,7243552,40366040,

%T 213357880,1178216264,6395922296,35375108728,194951335888

%N Number of winning length n strings with an 8-symbol alphabet in "same game".

%C Strings that can be reduced to null string by repeatedly removing an entire run of two or more consecutive symbols.

%C 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 b-ary strings with b >= 3, the same problem seems to be unsolved. - _Petros Hadjicostas_, Aug 31 2019

%H Chris Burns and Benjamin Purcell, <a href="/A035615/a035615.pdf">A note on Stephan's conjecture 77</a>, preprint, 2005. [Cached copy]

%H Chris Burns and Benjamin Purcell, <a href="https://www.fq.math.ca/Papers1/45-3/burns.pdf">Counting the number of winning strings in the 1-dimensional same game</a>, Fibonacci Quarterly, 45(3) (2007), 233-238.

%H Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/paper/same_game.ps">Polynomials in "same game"</a>, 2001. [ps file]

%H Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/paper/same_game.pdf"> Polynomials for same game</a>, 2001. [pdf file]

%H Ralf Stephan, <a href="https://arxiv.org/abs/math/0409509">Prove or disprove: 100 conjectures from the OEIS</a>, arXiv:math/0409509 [math.CO], 2004.

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

%Y Cf. A035615, A035617, A065237, A065238, A065239, A065240, A065242, A065243, A309874, A323812.

%Y Row b=8 of A323844.

%K nonn,more

%O 0,3

%A _Sascha Kurz_, Oct 23 2001

%E a(12)-a(17) from _Bert Dobbelaere_, Dec 26 2018