OFFSET
3,1
COMMENTS
a(n) is the number of minimal multiplex juggling patterns of period n using exactly 3 balls when we can catch/throw up to 2 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 = 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.: -(625*x^12 - 2206*x^11 + 4397*x^10 - 6648*x^9 + 7058*x^8 - 4674*x^7 + 1748*x^6 - 300*x^5 + 2*x^4 + 4*x^3)/(2600*x^13 - 21100*x^12 + 77590*x^11 - 171025*x^10 + 251874*x^9 - 261466*x^8 + 196626*x^7 - 108337*x^6 + 43682*x^5 - 12713*x^4 + 2592*x^3 - 350*x^2 + 28*x - 1).
MATHEMATICA
Rest[Rest[Rest[CoefficientList[Series[-(625 x^12 - 2206 x^11 + 4397 x^10 - 6648 x^9 + 7058 x^8 - 4674 x^7 + 1748 x^6 - 300 x^5 + 2 x^4 + 4 x^3)/(2600 x^13 - 21100 x^12 + 77590 x^11 - 171025 x^10 + 251874 x^9 - 261466 x^8 + 196626 x^7 - 108337 x^6 + 43682 x^5 - 12713 x^4 + 2592 x^3 - 350 x^2 + 28 x - 1), {x, 0, 33}], x]]]] (* Vincenzo Librandi, Jul 30 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jul 29 2015
STATUS
approved