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A133046
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Starting from the standard 12 against 12 starting position in checkers, the sequence gives the number of unique move sequences after n moves.
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2
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1, 7, 49, 302, 1469, 7361, 36768, 179740, 845931, 3963680, 18391564, 85242128, 388623673, 1766623630, 7978439499, 36263167175, 165629569428, 758818810990, 3493881706141, 16114043592799, 74545030871553, 345100524480819, 1602372721738102, 7437536860666213, 34651381875296000, 161067479882075800, 752172458688067137, 3499844183628002605, 16377718018836900735
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OFFSET
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0,2
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COMMENTS
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Duplicate captures (viz. the situation where a king can capture the same pieces in different directions) are counted separately.
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REFERENCES
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C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 512.
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LINKS
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Table of n, a(n) for n=0..28.
A. Bik, Aart's Computer Checkers Page
M. Fierz, CheckerBoard
I. Korshunov, Title?
Jonathan Schaeffer et al., Checkers is solved, Science, Vol. 317. no. 5844, pp. 1518-1522, Sep 14 2007.
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CROSSREFS
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Cf. A133047, A055213.
Sequence in context: A188986 A146884 A113235 * A200783 A188868 A126639
Adjacent sequences: A133043 A133044 A133045 * A133047 A133048 A133049
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KEYWORD
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nonn,nice
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AUTHOR
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Jonathan Schaeffer (jonathan(AT)cs.ualberta.ca), Dec 27 2007
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EXTENSIONS
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a(12) - a(20) computed by Aart Bik and sent by Richard Bean (oeis(AT)okuvrumo.fea.st), Sep 18 2009
a(21) - a(26) also computed by Aart Bik (ajcbik(AT)google.com), with last two completed Sept 18 2012. Rein Halbersma was first to compute a(22). Murray Cash confirmed Aart's a(23) and a(24) results.
a(27) - a(28) first computed by Aart Bik (ajcbik(AT)google.com), Sept 2012. Paul Byrne confirmed Aart's a(23) through a(28).
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STATUS
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approved
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