

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
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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

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. 15181522, Sep 14 2007.


CROSSREFS

Cf. A133047, A055213.
Sequence in context: A113235 A294261 A294293 * A200783 A267230 A188868
Adjacent sequences: A133043 A133044 A133045 * A133047 A133048 A133049


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).


STATUS

approved



