OFFSET
2,2
COMMENTS
a(n) is the number of minimal multiplex juggling patterns of period n using exactly 2 balls when we can catch/throw up to 2 balls at a time. (Minimal in the sense that each of the n throws is between 0 and n-1.)
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
Esther M. Banaian, Generalized Eulerian Numbers and Multiplex Juggling Sequences, (2016). All College Thesis Program. Paper 24.
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.
Index entries for linear recurrences with constant coefficients, signature (12,-59,155,-236,209,-100,20).
FORMULA
G.f.: -(5*x^6 - 3*x^5 - x^4 - x^3 + x^2)/(20*x^7 - 100*x^6 + 209*x^5 - 236*x^4 + 155*x^3 - 59*x^2 + 12*x - 1).
a(n) = 12*a(n-1) - 59*a(n-2) + 155*a(n-3) - 236*a(n-4) + 209*a(n-5) - 100*a(n-6) + 20*a(n-7). - Wesley Ivan Hurt, Jan 01 2024
MATHEMATICA
CoefficientList[Series[-(5*x^4 - 3*x^3 - x^2 - x + 1)/(20*x^7 - 100*x^6 + 209*x^5 - 236*x^4 + 155*x^3 - 59*x^2 + 12*x - 1), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 16 2015 *)
PROG
(PARI) Vec(-(5*x^6 - 3*x^5 - x^4 - x^3 + x^2)/(20*x^7 - 100*x^6 + 209*x^5 - 236*x^4 + 155*x^3 - 59*x^2 + 12*x - 1) + O(x^40)) \\ Michel Marcus, Aug 17 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Davis, Jul 29 2015
STATUS
approved