The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260584 Number of ways to place 4n rooks on n X n board, 4 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 4 rooks below the main diagonal. 6
1, 42, 1152, 22785, 358784, 4848569, 59160195, 674020718, 7332379979, 77311947872, 798116114567, 8122264310217, 81865063934240, 819786478839348, 8173571362926773, 81256681626746819, 806240597786756436, 7989356540290573170 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
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 4 balls at a time. (Minimal in the sense that the throws are between 0 and n-1.)
LINKS
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.: -(25340000*x^25 - 218339000*x^24 + 967516125*x^23 - 3006320955*x^22 + 7236534214*x^21 - 13729556248*x^20 + 20397063058*x^19 - 23597394968*x^18 + 21251854412*x^17 - 14962982713*x^16 + 8335966059*x^15 - 3793119227*x^14 + 1513380019*x^13 - 584800410*x^12 + 226357446*x^11 - 80585779*x^10 + 23590993*x^9 - 5268629*x^8 + 855872*x^7 - 97502*x^6 + 7700*x^5 - 464*x^4 + 26*x^3 - x^2)/(196000000*x^26 - 2903600000*x^25 + 20460490000*x^24 - 91266464000*x^23 + 289327787000*x^22 - 693785336400*x^21 + 1307696973825*x^20 - 1987649503130*x^19 + 2479934403745*x^18 - 2572088215962*x^17 + 2237510543313*x^16 - 1642726164623*x^15 + 1021902480875*x^14 - 539757845397*x^13 + 242151721153*x^12 - 92151943921*x^11 + 29657096575*x^10 - 8031745172*x^9 + 1817290072*x^8 - 340120209*x^7 + 51938261*x^6 - 6350073*x^5 + 605172*x^4 - 43205*x^3 + 2168*x^2 - 68*x + 1).
MATHEMATICA
CoefficientList[Series[-(25340000 x^23 -218339000 x^22 + 967516125 x^21 - 3006320955 x^20 + 7236534214 x^19 - 13729556248 x^18 + 20397063058 x^17 - 23597394968 x^16 + 21251854412 x^15 - 14962982713 x^14 + 8335966059 x^13 - 3793119227 x^12 + 1513380019 x^11 - 584800410 x^10 + 226357446 x^9 - 80585779 x^8 + 23590993 x^7 - 5268629 x^6 + 855872 x^5 - 97502 x^4 + 7700 x^3 - 464 x^2 + 26 x^1 - 1)/(196000000 x^26 - 2903600000 x^25 + 20460490000 x^24 - 91266464000 x^23 + 289327787000 x^22 - 693785336400 x^21 + 1307696973825 x^20 - 1987649503130 x^19 + 2479934403745 x^18 - 2572088215962 x^17 + 2237510543313 x^16 - 1642726164623 x^15 + 1021902480875 x^14 - 539757845397 x^13 + 242151721153 x^12 - 92151943921 x^11 + 29657096575 x^10 - 8031745172 x^9 + 1817290072 x^8 - 340120209 x^7 + 51938261 x^6 - 6350073 x^5 + 605172 x^4 - 43205 x^3 + 2168 x^2 -68 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 06 2015 *)
CROSSREFS
Sequence in context: A016094 A004361 A264178 * A004373 A001778 A111780
KEYWORD
nonn
AUTHOR
Jacob Landgraf, Jul 29 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 16:17 EDT 2024. Contains 372801 sequences. (Running on oeis4.)