%I #18 Aug 01 2022 08:09:02
%S 3,7,10,12,14,16,18,21,23,25,28,30,33,35,38,39,42,44,47,49,52,54,56,
%T 58,61,63,66,67,70,72,75,77,80,81,84,86,89,91,94,95,98,100,103,105,
%U 108,109,112,114,117,119,122,123
%N Longest checkmate in king and rook versus king endgame on an n X n chessboard.
%H V. Kotesovec, <a href="http://problem64.beda.cz/silo/kotesovec_icga_2001.pdf">King and Two Generalised Knights against King</a>, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001).
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Fairy chess endings on an n x n chessboard</a>, Electronic edition of chess booklets by Vaclav Kotesovec, vol. 8, pp. 360-361 (2013).
%F Conjecture: For n > 24, a(n) = 2*n - 3 + floor((n+1)/2) - floor(n/6).
%F a(n) ~ 7*n/3.
%e Longest win on an 8 X 8 chessboard: Ka1 Rb2 - Kc3, 1.Ka1-b1 Kc3-d4! 2.Kb1-c2! Kd4-c4 3.Rb2-b8 Kc4-d5 4.Kc2-d3! Kd5-e6 5.Kd3-d4 Ke6-f5 6.Rb8-e8! Kf5-f4 7.Re8-f8 Kf4-g5 8.Kd4-e4! Kg5-g6! 9.Ke4-f4 Kg6-g7! 10.Rf8-f5! Kg7-h6 11.Rf5-f6 Kh6-g7 12.Kf4-f5 Kg7-h7! 13.Rf6-f7 Kh7-h8! 14.Kf5-g5 Kh8-g8! 15.Kg5-g6! Kg8-h8! 16.Rf7-f8#, therefore a(8) = 16.
%Y Cf. A225551, A225553, A225554, A225555, A225556, A225557, A227437.
%K nonn
%O 3,1
%A _Vaclav Kotesovec_, May 10 2013
%E Terms a(52)-a(54) from _Vaclav Kotesovec_, May 17 2013