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A274458
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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.
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1
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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