A274458 White to move: Number of up to 5 man GBR-codes on an 8x8 chessboard having longest checkmate under perfect play in n moves if any such checkmate exists.

20, 6, 3, 8, 3, 2, 6, 5, 5, 4, 0, 1, 3, 1, 3, 6, 5, 0, 5, 3, 6, 2, 1, 3, 1, 1, 1, 6, 11, 7, 4, 3, 9, 3, 3, 2, 3, 2, 2, 7, 7, 0, 5, 1, 1, 0, 0, 0, 1, 3, 2, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 3, 2, 1, 2, 0, 1, 1, 3, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1

Offset: 1

Author

David A. Corneth, Jul 02 2016

Keywords

• nonn
• fini
• full

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.

Examples

			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.
		

Links

• k4it, All 6-men tables online (except 5 vs. 1).
• K. Kryukov, Longest checkmates
• Wikipedia, GBR code