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%I #40 Sep 02 2019 02:04:09
%S 1,0,3,3,15,33,105,297,879,2631,7833,23697,71385,216765,657849,
%T 2003151,6103743,18624693,56870385,173760513,531128349,1623881889,
%U 4965695331,15185222199,46435889601,141985777503
%N Number of winning length n strings with a 3-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_, Dec 27 2018
%H C. Burns and B. Purcell, <a href="/A035617/a035617_1.pdf">A note on Stephan's conjecture 77</a>, preprint, 2005.
%H C. Burns and B. 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="/A035617/a035617.pdf">Polynomials in "same game"</a>, 2001. [pdf file]
%e 11011001 is a winning string since 110{11}001 -> 11{000}1 -> {111} -> null.
%Y Cf. A035615, A065237, A065238, A065239, A065240, A065241, A065242, A065243.
%Y Row b=3 of A323844.
%K nonn,nice,more
%O 0,3
%A _Erich Friedman_
%E a(16)-a(25) from _Bert Dobbelaere_, Dec 26 2018
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