A252593 Number of ways to place 8 nonattacking queens on an n X n board.

0, 0, 0, 0, 0, 0, 0, 92, 13848, 636524, 14803480, 207667564, 2008758532, 14752426528, 87154016752, 432539436508, 1858901487620

Offset: 1

Author

Antal Pinter, Dec 18 2014

Keywords

• nonn
• hard
• more

Comments

Conjectured recurrence order is 477 (see "Non-attacking chess pieces", p. 19). - Vaclav Kotesovec, Dec 19 2014

Links

• S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, A q-Queens Problem, I. General theory, arXiv:1303.1879 [math.CO], 2013-2014.
• V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
• Antal Pinter, Combinatorics, software for enumerating positions of non-attacking chess pieces.
• I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.

Crossrefs

Cf. A000170, A036464, A047659, A061994, A108792, A176186, A178721.

Column k=8 of A348129.

Formula

a(n) = n^16/40320 - n^15/432 + 221*n^14/2160 + O(n^13). - Vaclav Kotesovec, Dec 19 2014

Extensions

a(16) from Vaclav Kotesovec, Dec 19 2014

a(17) from Vaclav Kotesovec, Dec 20 2014