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 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 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. 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 Cf. A260575, A260582, A260583, A260585, A260727. Sequence in context: A016094 A004361 A264178 * A004373 A001778 A111780 Adjacent sequences: A260581 A260582 A260583 * A260585 A260586 A260587 KEYWORD nonn AUTHOR Jacob Landgraf, Jul 29 2015 STATUS approved

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