A274683 White to move: King, Knight and Bishop vs. King: Number of positions with mate in n.

1840, 1200, 3216, 15960, 39752, 45192, 48396, 40408, 42720, 56240, 95208, 142084, 189592, 190296, 139684, 118004, 114200, 119780, 127480, 216552, 350136, 484868, 576832, 584456, 729040, 949808, 1278384, 1531500, 1434268, 859400, 261004, 33580, 1104

Offset

1,1

Comments

After n = 33, all terms are 0 so the sequence ends at n = 33.

GBR code is 0011. Longest checkmate under perfect play is in 33 (FEN 8/8/7N/8/8/8/8/K1k1B3 w - - 0 1). For path of moves, see k4it-link. Data is found using Kryukov link, "Endgame Tablebases online". FEN is found in Kryukov link, "Longest checkmates in chess".

The listed examples, or more generally up to 6 man positions can be examined using the k4it link.

References

Christian Posthoff, Günter Reinemann, Computerschach-Schachcomputer, Akademie-Verlag Berlin 1987, p. 52.

Links

Table of n, a(n) for n=1..33.

S. T. Dekker and H. J. van den Herik, GBR class 0011: a 33-move endgame, EG 78, 1984, p. 345-7.

Steven J. Edwards, Endgame tablebase position count summaries, 1994.

k4it, All 6-men tables online (except 5 vs. 1).

K. Kryukov, Endgame Tablebases Online

K. Kryukov, Longest checkmates in chess

Wikipedia, GBR code

Crossrefs

Cf. A225556, A274684.

Sequence in context: A100970 A159202 A238294 * A231079 A257319 A287172

Adjacent sequences: A274680 A274681 A274682 * A274684 A274685 A274686

Keyword

nonn,fini,full

Author

David A. Corneth, Jul 02 2016

Extensions

Data and comments changed by Vaclav Kotesovec, Aug 01 2016

Status

approved