A225552 Longest checkmate in king and rook versus king endgame on an n X n chessboard.

3, 7, 10, 12, 14, 16, 18, 21, 23, 25, 28, 30, 33, 35, 38, 39, 42, 44, 47, 49, 52, 54, 56, 58, 61, 63, 66, 67, 70, 72, 75, 77, 80, 81, 84, 86, 89, 91, 94, 95, 98, 100, 103, 105, 108, 109, 112, 114, 117, 119, 122, 123

Offset

3,1

Links

Table of n, a(n) for n=3..54.

V. Kotesovec, King and Two Generalised Knights against King, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001).

V. Kotesovec, Fairy chess endings on an n x n chessboard, Electronic edition of chess booklets by Vaclav Kotesovec, vol. 8, pp. 360-361 (2013), pp. 540-541 (second edition, 2017).

Formula

Conjecture: For n > 24, a(n) = 2*n - 3 + floor((n+1)/2) - floor(n/6).

a(n) ~ 7*n/3.

Example

Longest win on an 8 X 8 chessboard: Ka1 Rb2 - Kc3, 1.Ka1-b1 Kc3-d4! 2.Kb1-c2! Kd4-c4 3.Rb2-b8 Kc4-d5 4.Kc2-d3! Kd5-e6 5.Kd3-d4 Ke6-f5 6.Rb8-e8! Kf5-f4 7.Re8-f8 Kf4-g5 8.Kd4-e4! Kg5-g6! 9.Ke4-f4 Kg6-g7! 10.Rf8-f5! Kg7-h6 11.Rf5-f6 Kh6-g7 12.Kf4-f5 Kg7-h7! 13.Rf6-f7 Kh7-h8! 14.Kf5-g5 Kh8-g8! 15.Kg5-g6! Kg8-h8! 16.Rf7-f8#, therefore a(8) = 16.

Crossrefs

Cf. A225551, A225553, A225554, A225555, A225556, A225557, A227437.

Sequence in context: A363245 A276117 A105135 * A147683 A319279 A013574

Adjacent sequences: A225549 A225550 A225551 * A225553 A225554 A225555

Keyword

nonn

Author

Vaclav Kotesovec, May 10 2013

Extensions

Terms a(52)-a(54) from Vaclav Kotesovec, May 17 2013

Status

approved