A115229 - OEIS

%I #5 Mar 31 2012 20:35:52

%S 3,12,16,31,21,44,3,6

%N Number of ways in chess to force mate in n moves for a single knight against a single pawn, without duals, without short mates and excluding rotations, mirroring and color reversing.

%C The mate is only possible against a pawn on a border line (a-line or h-line).

%C No non-dual (single solution) mates are possible beyond n = 7 (cf. Springerzauber, page 178).

%C Obviously the positions with the higher number of moves lead via a unique chain of positions with the lower numbers.

%D John Selman and Harrie Grondijs, Springerzauber, 1998, chapter 16.

%e Example: The three positions with 0 moves (checkmate) are:

%e a) White: Kc2, Nb3, Black: Ka1, Pawn a2

%e b) White: Kc1, Nb3, Black: Ka1, Pawn a2

%e c) White: Kc1, Nc2, Black: Ka1, pawn a2

%K nonn

%O 0,1

%A _N. J. A. Sloane_, based on email from _Harrie Grondijs_, Mar 06 2006