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A035617 Number of winning length n strings with a 3-symbol alphabet in "same game". 14
1, 0, 3, 3, 15, 33, 105, 297, 879, 2631, 7833, 23697, 71385, 216765, 657849, 2003151, 6103743, 18624693, 56870385, 173760513, 531128349, 1623881889, 4965695331, 15185222199, 46435889601, 141985777503 (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, Dec 27 2018

LINKS

Table of n, a(n) for n=0..25.

C. Burns and B. Purcell, A note on Stephan's conjecture 77, preprint, 2005.

C. Burns and B. 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 in "same game", 2001. [pdf file]

EXAMPLE

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

CROSSREFS

Cf. A035615, A065237, A065238, A065239, A065240, A065241, A065242, A065243.

Row b=3 of A323844.

Sequence in context: A127328 A002891 A089875 * A126319 A165553 A056314

Adjacent sequences:  A035614 A035615 A035616 * A035618 A035619 A035620

KEYWORD

nonn,nice,more

AUTHOR

Erich Friedman

EXTENSIONS

a(16)-a(25) from Bert Dobbelaere, Dec 26 2018

STATUS

approved

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Last modified July 10 00:05 EDT 2020. Contains 335570 sequences. (Running on oeis4.)