A133046 Starting from the standard 12 against 12 starting position in checkers, the sequence gives the number of distinct move sequences after n moves.

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

Author

Jonathan Schaeffer (jonathan(AT)cs.ualberta.ca), Dec 27 2007

Keywords

• nonn
• nice

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

• A. Bik, Aart's Computer Checkers Page
• M. Fierz, CheckerBoard
• I. Korshunov, Standard correctness check for a move generator [in Russian]
• Jonathan Schaeffer et al., Checkers is solved, Science, Vol. 317. no. 5844, pp. 1518-1522, Sep 14 2007.

Crossrefs

Cf. A133047, A055213.

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