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A065238 Number of winning length n strings with a 5-symbol alphabet in "same game". 11
1, 0, 5, 5, 45, 105, 545, 1825, 7965, 30845, 128945, 527785, 2202785, 9222985, 38818505, 164436125, 698347645, 2981306665, 12756855065 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=0..18.

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.


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


Cf. A035615, A035617, A065237, A065239, A065240, A065241, A065242, A065243, A309874, A323812.

Row b=5 of A323844.

Sequence in context: A271117 A271297 A178693 * A196388 A073128 A189749

Adjacent sequences: A065235 A065236 A065237 * A065239 A065240 A065241




Sascha Kurz, Oct 23 2001


a(13)-a(18) from Bert Dobbelaere, Dec 26 2018



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Last modified December 9 17:12 EST 2022. Contains 358702 sequences. (Running on oeis4.)