A179063 Number of non-attacking placements of 8 rooks on an n X n board.
0, 0, 0, 0, 0, 0, 0, 40320, 3265920, 81648000, 1097712000, 9879408000, 66784798080, 363606122880, 1669619952000, 6678479808000, 23828156352000, 77203226580480, 230333593351680, 639815537088000, 1669577821632000, 4122835028928000
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016
- Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
Programs
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PARI
a(n) = 8!*binomial(n, 8)^2 \\ Andrew Howroyd, Feb 13 2018
Formula
a(n) = 8!*binomial(n,8)^2.
G.f.: -40320*x^8*(x^8 +64*x^7 +784*x^6 +3136*x^5 +4900*x^4 +3136*x^3 +784*x^2 +64*x +1) / (x -1)^17. - Colin Barker, Jan 08 2013