A225551 Longest checkmate in king and queen versus king endgame on an n X n chessboard.

1, 4, 6, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57

Offset

3,2

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.359 (2013), p. 539 (second edition, 2017).

Formula

Conjecture: For n > 8, a(n) = 2*n-3-floor(n/2).

a(n) ~ 3*n/2.

Empirical g.f.: x^3*(x^8-x^7+x^5-x^4-2*x^3+x^2+3*x+1) / ((x-1)^2*(x+1)). - Colin Barker, May 11 2013

Example

Longest win on an 8x8 chessboard: Ka1 Qb2 - Kf5, 1.Ka1-b1 Kf5-e6! 2.Kb1-c2 Ke6-f5! 3.Kc2-c3 Kf5-e6 4.Kc3-d4! Ke6-f5 5.Qb2-b6! Kf5-g4 6.Kd4-e4 Kg4-g5! 7.Qb6-c6 Kg5-h4 8.Ke4-f4 Kh4-h5! 9.Qc6-d6 Kh5-h4! 10.Qd6-h6#, therefore a(8) = 10.

Crossrefs

Cf. A225552, A225553, A225554, A225555, A225556, A225557, A227437.

Sequence in context: A181057 A151757 A171413 * A247359 A305415 A105432

Adjacent sequences: A225548 A225549 A225550 * A225552 A225553 A225554

Keyword

nonn

Author

Vaclav Kotesovec, May 10 2013

Status

approved