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

1,1

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

Table of n, a(n) for n=1..127.

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

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

Sequence in context: A201137 A040385 A161997 * A351025 A327131 A076594

Adjacent sequences: A274455 A274456 A274457 * A274459 A274460 A274461

Keyword

nonn,fini,full

Author

David A. Corneth, Jul 02 2016

Status

approved