

A274458


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


1



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
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OFFSET

1,1


COMMENTS

Numbers and examples derived from Kryukovlink.
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 6men 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 * A327131 A076594 A174991
Adjacent sequences: A274455 A274456 A274457 * A274459 A274460 A274461


KEYWORD

nonn,fini,full


AUTHOR

David A. Corneth, Jul 02 2016


STATUS

approved



