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Search: id:A035615
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| A035615 |
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Number of winning n-digit binary strings in "same game". |
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13
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| 0, 2, 2, 6, 12, 26, 58, 126, 278, 602, 1300, 2774, 5878, 12350, 25778, 53470, 110332, 226610, 463602, 945214, 1921550, 3896642, 7885092, 15927086, 32121582, 64697726
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Strings that can be reduced to null string by repeatedly removing an entire run of two or more consecutive digits.
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LINKS
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C. Burns and B. Purcell, A note on Stephan's conjecture 77, preprint, 2005.
Sascha Kurz, Polynomials for same game, pdf
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FORMULA
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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.
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EXAMPLE
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11011001 is a winning string since 110{11}001->11{000}1->{111}->null
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CROSSREFS
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Cf. A035617.
Adjacent sequences: A035612 A035613 A035614 this_sequence A035616 A035617 A035618
Sequence in context: A091764 A079005 A054481 this_sequence A115962 A019311 A052994
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KEYWORD
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hard,nonn,nice
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 09 2001
Further terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Oct 19 2001
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