%I A035615
%S A035615 0,2,2,6,12,26,58,126,278,602,1300,2774,5878,12350,25778,53470,110332,
%T A035615 226610,463602,945214,1921550,3896642,7885092,15927086,32121582,
%U A035615 64697726
%N A035615 Number of winning n-digit binary strings in "same game".
%C A035615 Strings that can be reduced to null string by repeatedly removing an 
               entire run of two or more consecutive digits.
%H A035615 C. Burns and B. Purcell, <a href="http://www.oberlin.edu/math/Research/
               Burns-Purcell.pdf">A note on Stephan's conjecture 77</a>, preprint, 
               2005.
%H A035615 Sascha Kurz, Polynomials for same game, <a href="http://www.mathe2.uni-bayreuth.de/
               sascha/oeis/paper/same_game.pdf">pdf</a>
%F A035615 G.f.: x(2x^6-6x^5+8x^4+2x^3-6x^2+2x)/[(1-x^2)(1-2x)(1-x-x^2)^2] (conjectured). 
               - R. Stephan, May 11 2004. Established by Burns and Purcell - see 
               link.
%e A035615 11011001 is a winning string since 110{11}001->11{000}1->{111}->null
%Y A035615 Cf. A035617.
%Y A035615 Sequence in context: A156992 A054481 A157285 this_sequence A115962 A019311 
               A052994
%Y A035615 Adjacent sequences: A035612 A035613 A035614 this_sequence A035616 A035617 
               A035618
%K A035615 hard,nonn,nice
%O A035615 1,2
%A A035615 Erich Friedman (erich.friedman(AT)stetson.edu)
%E A035615 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 09 
               2001
%E A035615 Further terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Oct 
               19 2001