A260583 Number of ways to place 3n rooks on an n X n board, 3 rooks in each row and each column, multiple rooks in an allowed cell, and exactly 4 rooks below the main diagonal.

11, 595, 14679, 253247, 3564803, 44226950, 505572550, 5473391465, 57122380066, 581477852342, 5819301681925, 57564437594318, 564911137682637, 5513703983635512, 53616132982114742, 520057429817203110, 5035740328012627416, 48704838658567681135

Offset

3,1

Comments

a(n) is the number of minimal multiplex juggling patterns of period n using exactly 4 balls when we can catch/throw up to 3 balls at a time. (Minimal in the sense that the throw heights are between 0 and n-1.)

Links

Colin Barker, Table of n, a(n) for n = 3..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.

Formula

G.f.: -(24558000*x^24 - 221169800*x^23 + 1030045255*x^22 - 3270869391*x^21 + 7705144467*x^20 - 13843184523*x^19 + 19209151138*x^18 - 20800159606*x^17 + 17768204859*x^16 - 12126221923*x^15 + 6718636422*x^14 - 3086566305*x^13 + 1204914514*x^12 - 407103232*x^11 + 118646908*x^10 - 28836372*x^9 + 5505383*x^8 - 758705*x^7 + 65305*x^6 - 2162*x^5 - 131*x^4 + 11*x^3)/(133600000*x^25 - 1875920000*x^24 + 12500686000*x^23 - 52604444000*x^22 + 156920670600*x^21 - 353103818000*x^20 + 622718972395*x^19 - 882777307660*x^18 + 1023713051333*x^17 - 983132187597*x^16 + 788634518440*x^15 - 531447118763*x^14 + 301890662895*x^13 - 144761728498*x^12 + 58568440406*x^11 - 19945788669*x^10 + 5692551701*x^9 - 1352405718*x^8 + 264899104*x^7 - 42210805*x^6 + 5370925*x^5 - 531418*x^4 + 39303*x^3 - 2039*x^2 + 66*x - 1).

Crossrefs

Column k=4 of A269743.

Cf. A260575, A260582, A260584, A260585, A260727.

Sequence in context: A263184 A370087 A288326 * A079915 A185656 A142738

Adjacent sequences: A260580 A260581 A260582 * A260584 A260585 A260586

Keyword

nonn

Author

Esther Banaian, Jul 29 2015

Status

approved