%I #13 Sep 12 2015 13:59:03
%S 0,1,2,3,4,4,5,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,
%T 16,17,17,18,18,19,19,20,20,21
%N Longest checkmate in king and amazon versus king endgame on an n X n chessboard.
%C An amazon (superqueen) moves like a queen and a knight.
%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.364 (2013)
%F Conjecture: for n > 10, a(n) = floor((n+2)/2).
%F Empirical g.f.: -x^4*(x^9-x^8+x^4-x-1) / ((x-1)^2*(x+1)). - _Colin Barker_, May 11 2013
%e Longest win on an 8x8 chessboard: Ka1 AMb1 - Kd4, 1.AMb1-f5! Kd4-c4! 2.Ka1-b1 Kc4-b4! 3.Kb1-b2 Kb4-a4 4.AMf5-c5#, therefore a(8) = 4.
%Y Cf. A172200, A051223, A178967, A225551, A225552, A225554, A225555, A225556, A225557, A227437.
%K nonn
%O 3,3
%A _Vaclav Kotesovec_, May 10 2013