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 A065240 Number of winning length n strings with a 7-symbol alphabet in "same game". 11
 1, 0, 7, 7, 91, 217, 1561, 5593, 32011, 139363, 732697, 3492265, 17899609, 89014933, 455041825, 2311847083, 11875575355, 61080825757 (list; graph; refs; listen; history; text; internal format)
 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 b-ary strings with b >= 3, the same problem seems to be unsolved. - Petros Hadjicostas, Aug 31 2019 LINKS 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 1-dimensional same game, Fibonacci Quarterly, 45(3) (2007), 233-238. 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

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Last modified January 23 01:30 EST 2020. Contains 331166 sequences. (Running on oeis4.)