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