OFFSET
1,1
COMMENTS
Numbers and examples derived from Kryukov-link.
Longest 3 man mate is King and Pawn vs. King (GBR code 0000.10) in 28, with FEN 8/8/8/1k6/8/8/K5P1/8 w - - 0 1.
Longest 4 man mate is King and Pawn vs. King and rook (GBR code 0300.10) in 43, with FEN 8/5k2/2PK4/5r2/8/8/8/8 w - - 0 1
Longest 5 man mate is King and 2 Pawns vs. King and Pawn in 127 (GBR code 0000.12), with 8/8/8/8/1p2P3/4P3/1k6/3K4 w - - 0 1. As the sequence is up to 5 man, this makes 127 the length of the sequence.
For some particular material counted, it needn't be a guaranteed win under perfect play. For example King and Knight vs King and Knight (GBR code 0004) generally is a draw, but a forced checkmate in one exists (FEN 8/8/8/8/8/8/n1K5/k1N5 w - - 0 1).
The listed examples, or more generally up to 6 man positions can be examined using the k4it link.
After n = 127, all terms are 0 so the sequence ends at n = 127.
LINKS
K. Kryukov, Longest checkmates
Wikipedia, GBR code
EXAMPLE
a(2) = 6 because there are 6 positions in which the longest checkmate under perfect play with (at most) 5 man is in two moves. The six configurations are: KBKQB, KBKQP, KBKRB, KBKRP, KBKBB and KBKBN.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
David A. Corneth, Jul 02 2016
STATUS
approved