A225554 Longest checkmate in king and empress versus king endgame on an n X n chessboard.

3, 5, 7, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 25, 26, 28, 30, 32, 34, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 53, 55, 57, 59, 61, 63, 64, 66, 68

Offset

3,1

Comments

An empress moves like a rook and a knight.

Links

Table of n, a(n) for n=3..40.

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.363 (2013)

Formula

Conjecture: a(n) ~ 7*n/4.

Example

Longest win on an 8x8 chessboard: Ka1 EMb1 - Kd4, 1.Ka1-a2 Kd4-e5 2.Ka2-b3 Ke5-f4 3.Kb3-c3 Kf4-e5 4.EMb1-b6! Ke5-f4 5.Kc3-d4 Kf4-g5 6.Kd4-e4 Kg5-g4! 7.EMb6-e6 Kg4-g3! 8.EMe6-f4! Kg3-h2! 9.Ke4-f3! Kh2-g1! 10.Kf3-g3 Kg1-h1! 11.EMf4-f1#, therefore a(8) = 11.

Crossrefs

Cf. A137774, A218244, A225551, A225552, A225553, A225555, A225556, A225557, A227437.

Sequence in context: A171508 A049068 A185602 * A257019 A071977 A183423

Adjacent sequences: A225551 A225552 A225553 * A225555 A225556 A225557

Keyword

nonn

Author

Vaclav Kotesovec, May 10 2013

Status

approved