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A133046
Starting from the standard 12 against 12 starting position in checkers, the sequence gives the number of distinct move sequences after n moves.
2
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, 76309690522352444005
OFFSET
0,2
COMMENTS
Duplicate captures (viz. the situation where a king can capture the same pieces in different directions) are counted separately.
REFERENCES
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 512.
LINKS
M. Fierz, CheckerBoard
I. Korshunov, Title?
Jonathan Schaeffer et al., Checkers is solved, Science, Vol. 317. no. 5844, pp. 1518-1522, Sep 14 2007.
CROSSREFS
Sequence in context: A294261 A294293 A357146 * A200783 A267230 A188868
KEYWORD
nonn,nice
AUTHOR
Jonathan Schaeffer (jonathan(AT)cs.ualberta.ca), Dec 27 2007
EXTENSIONS
a(12)-a(20) computed by Aart Bik and sent by Richard Bean, Sep 18 2009
a(21)-a(26) computed by Aart Bik, with last two completed Sep 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, Sep 2012. Paul Byrne confirmed Aart's a(23)-a(28).
a(29) from Murray Cash, Nov 20 2020
STATUS
approved