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 A225556 Longest checkmate in king, bishop and knight versus king endgame on an n X n chessboard. 8
 7, 14, 13, 22, 21, 33, 29, 47, 39, 64, 50, 78, 63, 93, 76, 112, 90, 131, 105, 151, 121, 171 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Julius Telesin, Can B + S give checkmate on 1000 x 1000 chessboard?, EG 73, 1983, p.190 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.224 and 231 (2013) FORMULA Conjecture: a(n) ~ n^2/6+3*n if n is even and a(n) ~ n^2/6+2*n if n is odd. EXAMPLE Longest win on an 8x8 chessboard: Ka1 Bc1 Sb1 - Kc2, 1.Bc1-d2 Kc2-b3! 2.Bd2-f4 Kb3-c2! 3.Ka1-a2! Kc2-d3! 4.Ka2-b3! Kd3-e4 5.Bf4-h2 Ke4-d5 6.Kb3-c3 Kd5-e4 7.Sb1-d2! Ke4-d5! 8.Kc3-d3! Kd5-c5! 9.Sd2-c4! Kc5-b5 10.Kd3-d4 Kb5-c6! 11.Bh2-g3 Kc6-b7! 12.Kd4-d5 Kb7-a7! 13.Kd5-c6! Ka7-a6 14.Bg3-h2 Ka6-a7! 15.Sc4-b6! Ka7-a6! 16.Bh2-b8! Ka6-a5! 17.Sb6-d5! Ka5-a4! 18.Kc6-c5 Ka4-b3! 19.Sd5-b4! Kb3-b2! 20.Bb8-f4! Kb2-c3! 21.Bf4-g5 Kc3-b3! 22.Bg5-f6 Kb3-a4 23.Kc5-c4! Ka4-a5! 24.Bf6-d8! Ka5-a4! 25.Sb4-d3! Ka4-a3! 26.Bd8-e7 Ka3-a4! 27.Sd3-c5! Ka4-a3! 28.Kc4-c3! Ka3-a2! 29.Sc5-d3! Ka2-b1! 30.Kc3-b3! Kb1-a1! 31.Kb3-c2! Ka1-a2! 32.Sd3-c1! Ka2-a1! 33.Be7-f6#, therefore a(8) = 33. CROSSREFS Cf. A225551, A225552, A225553, A225554, A225555, A225557, A227437. Sequence in context: A196178 A269161 A307964 * A064666 A269160 A286418 Adjacent sequences:  A225553 A225554 A225555 * A225557 A225558 A225559 KEYWORD nonn,hard,more AUTHOR Vaclav Kotesovec, May 10 2013 EXTENSIONS a(21) from Vaclav Kotesovec, Jan 11 2017 a(22) from Vaclav Kotesovec, Jan 15 2017 a(23) from Vaclav Kotesovec, Jun 22 2017 a(24) from Vaclav Kotesovec, Jun 30 2017 STATUS approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)