A260727 Number of ways to place 3n rooks on an n X n board, with 3 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 3 rooks below the main diagonal.
1, 23, 325, 3368, 28819, 218788, 1539399, 10314315, 66953292, 425761614, 2671506918, 16618186770, 102796975770, 633596982417, 3896224129259, 23924104985984, 146764696175937, 899809941054468, 5514653407814317, 33789681789605283, 207007665004469906
Offset: 2
Links
- Colin Barker, Table of n, a(n) for n = 2..1000
- E. Banaian, S. Butler, C. Cox, J. Davis, J. Landgraf and S. Ponce, A generalization of Eulerian numbers via rook placements, arXiv:1508.03673 [math.CO], 2015.
Programs
-
Mathematica
CoefficientList[Series[-(700*x^13 - 2435*x^12 + 4558*x^11 - 7532*x^10 + 10404*x^9 - 9697*x^8 + 5545*x^7 - 1844*x^6 + 336*x^5 - 39*x^4 + 7*x^3 - x^2)/((x^2)*(4000*x^14 - 35400*x^13 + 143100*x^12 - 349910*x^11 + 577675*x^10 - 680496*x^9 + 589248*x^8 - 380592*x^7 + 184037*x^6 - 66214*x^5 + 17423*x^4 - 3246*x^3 + 404*x^2 - 30*x + 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jul 30 2015 *)
Formula
G.f.: -(700*x^13 - 2435*x^12 + 4558*x^11 - 7532*x^10 + 10404*x^9 - 9697*x^8 + 5545*x^7 - 1844*x^6 + 336*x^5 - 39*x^4 + 7*x^3 - x^2)/(4000*x^14 - 35400*x^13 + 143100*x^12 - 349910*x^11 + 577675*x^10 - 680496*x^9 + 589248*x^8 - 380592*x^7 + 184037*x^6 - 66214*x^5 + 17423*x^4 - 3246*x^3 + 404*x^2 - 30*x + 1).
Comments