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A179061
Number of non-attacking placements of 6 rooks on an n X n board.
4
0, 0, 0, 0, 0, 720, 35280, 564480, 5080320, 31752000, 153679680, 614718720, 2120152320, 6492966480, 18036018000, 46172206080, 110279070720, 248127909120, 530024705280, 1081683072000, 2120098821120, 4008311833680
OFFSET
1,6
LINKS
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).
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
PROG
(PARI) a(n) = 6! * binomial(n, 6)^2 \\ Andrew Howroyd, Feb 13 2018
CROSSREFS
Column k=5 of A144084.
Cf. A179060 (5 rooks), A179062 (7 rooks).
Sequence in context: A052720 A166759 A181504 * A342074 A055361 A092716
KEYWORD
easy,nonn
AUTHOR
Thomas Zaslavsky, Jun 27 2010
STATUS
approved