

A225551


Longest checkmate in king and queen versus king endgame on an n X n chessboard.


8



1, 4, 6, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57
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OFFSET

3,2


LINKS



FORMULA

Conjecture: For n > 8, a(n) = 2*n3floor(n/2).
a(n) ~ 3*n/2.
Empirical g.f.: x^3*(x^8x^7+x^5x^42*x^3+x^2+3*x+1) / ((x1)^2*(x+1)).  Colin Barker, May 11 2013


EXAMPLE

Longest win on an 8x8 chessboard: Ka1 Qb2  Kf5, 1.Ka1b1 Kf5e6! 2.Kb1c2 Ke6f5! 3.Kc2c3 Kf5e6 4.Kc3d4! Ke6f5 5.Qb2b6! Kf5g4 6.Kd4e4 Kg4g5! 7.Qb6c6 Kg5h4 8.Ke4f4 Kh4h5! 9.Qc6d6 Kh5h4! 10.Qd6h6#, therefore a(8) = 10.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



