A115229 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.

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

Offset

0,1

Comments

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

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

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

References

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

Links

Table of n, a(n) for n=0..7.

Example

Example: The three positions with 0 moves (checkmate) are:
a) White: Kc2, Nb3, Black: Ka1, Pawn a2
b) White: Kc1, Nb3, Black: Ka1, Pawn a2
c) White: Kc1, Nc2, Black: Ka1, pawn a2

Crossrefs

Sequence in context: A277738 A064106 A022411 * A224924 A136047 A082965

Adjacent sequences: A115226 A115227 A115228 * A115230 A115231 A115232

Keyword

nonn

Author

N. J. A. Sloane, based on email from Harrie Grondijs, Mar 06 2006

Status

approved