A225557 Longest checkmate in king and two bishops versus king endgame on an n X n chessboard.

1, 9, 11, 13, 16, 19, 21, 24, 26, 29, 32, 35, 38, 40, 44, 46, 49, 52, 55, 58

Offset

3,2

Links

Table of n, a(n) for n=3..22.

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, p.225 and 236 (2013)

Formula

Conjecture: a(n) ~ 11*n/4.

Example

Longest win on an 8x8 chessboard: Ka1 Bd1 Bb4 - Kc4, 1.Bb4-d6 Kc4-d5! 2.Bd6-g3 Kd5-c6 3.Ka1-b1 Kc6-d5 4.Kb1-c1 Kd5-c6 5.Kc1-c2 Kc6-d5 6.Kc2-d3! Kd5-e6 7.Kd3-e4! Ke6-e7 8.Ke4-e5 Ke7-d7! 9.Ke5-d5 Kd7-e8 10.Bd1-h5 Ke8-e7 11.Bg3-e5! Ke7-d8 12.Kd5-d6! Kd8-c8! 13.Kd6-c6! Kc8-d8! 14.Be5-f6 Kd8-c8! 15.Bh5-g6 Kc8-b8! 16.Kc6-b6! Kb8-a8 17.Bg6-f5 Ka8-b8! 18.Bf6-e5! Kb8-a8! 19.Bf5-e4#, therefore a(8) = 19.

Crossrefs

Cf. A225551, A225552, A225553, A225554, A225555, A225556, A227437.

Sequence in context: A251394 A155877 A214865 * A120177 A291350 A289697

Adjacent sequences: A225554 A225555 A225556 * A225558 A225559 A225560

Keyword

nonn,hard,more

Author

Vaclav Kotesovec, May 10 2013

Extensions

a(21)-a(22) from Vaclav Kotesovec, Jan 11 2017

Status

approved