%I #15 Sep 12 2015 13:57:18
%S 1,4,6,7,8,10,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,35,36,
%T 38,39,41,42,44,45,47,48,50,51,53,54,56,57
%N Longest checkmate in king and queen 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, p.359 (2013)
%F Conjecture: For n > 8, a(n) = 2*n-3-floor(n/2).
%F a(n) ~ 3*n/2.
%F Empirical g.f.: x^3*(x^8-x^7+x^5-x^4-2*x^3+x^2+3*x+1) / ((x-1)^2*(x+1)). - _Colin Barker_, May 11 2013
%e Longest win on an 8x8 chessboard: Ka1 Qb2 - Kf5, 1.Ka1-b1 Kf5-e6! 2.Kb1-c2 Ke6-f5! 3.Kc2-c3 Kf5-e6 4.Kc3-d4! Ke6-f5 5.Qb2-b6! Kf5-g4 6.Kd4-e4 Kg4-g5! 7.Qb6-c6 Kg5-h4 8.Ke4-f4 Kh4-h5! 9.Qc6-d6 Kh5-h4! 10.Qd6-h6#, therefore a(8) = 10.
%Y Cf. A225552, A225553, A225554, A225555, A225556, A225557, A227437.
%K nonn
%O 3,2
%A _Vaclav Kotesovec_, May 10 2013