A179064 Number of non-attacking placements of 9 rooks on an n X n board.

0, 0, 0, 0, 0, 0, 0, 0, 362880, 36288000, 1097712000, 17563392000, 185513328000, 1454424491520, 9090153072000, 47491411968000, 214453407168000, 857813628672000, 3096707199505920, 10237048593408000, 31350961317312000

Offset

1,9

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 (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).

Formula

a(n) = 9!*binomial(n,9)^2.

G.f.: -362880*x^9*(x +1)*(x^8 +80*x^7 +1216*x^6 +5840*x^5 +10036*x^4 +5840*x^3 +1216*x^2 +80*x +1) / (x -1)^19. - Colin Barker, Jan 08 2013

Prog

(PARI) a(n) = 9! * binomial(n, 9)^2 \\ Andrew Howroyd, Feb 13 2018

Crossrefs

Column k=9 of A144084.

Cf. A179063 (8 rooks), A179065 (10 rooks).

Sequence in context: A254082 A228912 A213871 * A246197 A246617 A246220

Adjacent sequences: A179061 A179062 A179063 * A179065 A179066 A179067

Keyword

easy,nonn

Author

Thomas Zaslavsky, Jun 28 2010

Status

approved