Jeffrey Davis has authored 2 sequences.
A260752
Number of prime juggling patterns of period n using 5 balls.
Original entry on oeis.org
1, 5, 29, 157, 901, 4822, 27447, 149393, 836527, 4610088, 25846123, 142296551, 799268609, 4426204933, 24808065829, 137945151360, 773962487261, 4310815784117, 24208263855765
Offset: 1
In siteswap notation, the prime juggling pattern(s) of length one is 5; of length two are 64, 73, 82, 91 and (10)0; of length three are (11)31, (11)22, 4(10)1, 3(12)0, (13)20, (13)11, 591, (10)23, (10)41, 960, 780, 663, 744, 753, 4(11)0, (12)12, (12)30, 771, 861, (15)00, 933, 942, 582, (10)50, 690, (14)01, 852, 834 and 672.
- Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce, Counting prime juggling patterns, arXiv:1508.05296 [math.CO], 2015.
- Jack Boyce, jprime program, 2024.
- Fan Chung and R. L. Graham, Primitive juggling sequences, American Mathematical Monthly 115 (2008), 185-194.
A260585
Number of ways to place 2n rooks on an n X n board, with 2 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 2 rooks below the main diagonal.
Original entry on oeis.org
1, 11, 72, 367, 1630, 6680, 26082, 98870, 368045, 1354850, 4953503, 18035279, 65499031, 237511321, 860471110, 3115667369, 11277816388, 40814611818, 147692103728, 534404499040, 1933597628291, 6996040095316, 25312367524557, 91581960107817, 331348634005165
Offset: 2
- 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).
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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 *)
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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
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