A179061 Number of non-attacking placements of 6 rooks on an n X n board.
0, 0, 0, 0, 0, 720, 35280, 564480, 5080320, 31752000, 153679680, 614718720, 2120152320, 6492966480, 18036018000, 46172206080, 110279070720, 248127909120, 530024705280, 1081683072000, 2120098821120, 4008311833680
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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Programs
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PARI
a(n) = 6! * binomial(n, 6)^2 \\ Andrew Howroyd, Feb 13 2018
Formula
a(n) = 6! * binomial(n, 6)^2.
G.f.: -720*x^6*(x^6+36*x^5+225*x^4+400*x^3+225*x^2+36*x+1) / (x-1)^13. - Colin Barker, Jan 08 2013