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A370306
Number of multiplex juggling cards with n balls and capacity 3.
1
1, 2, 7, 24, 70, 198, 532, 1370, 3418, 8296, 19677, 45770, 104687, 235972, 525136, 1155516, 2517199, 5434454, 11638099, 24741812, 52250956, 109678746, 228948036, 475479494, 982831024, 2022696684, 4145947065, 8466032502, 17226979885, 34939008232, 70643799296, 142423352600
OFFSET
0,2
LINKS
S. Butler, J. Choi, K. Kim, and K. Seo, Enumerating multiplex juggling patterns, J. Integer Seq., 22(1):Art. 19.1.7, 21, 2019.
Y. Cho, J. Kim, J. S. Kim, and N. Lee, Enumeration of multiplex juggling card sequences using generalized q-derivatives, arXiv:2402.09903 [math.CO], 2014.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,-7,8,12,8,-7,-12,-10,-4,-1).
FORMULA
G.f.: (1-2*x+x^2+4*x^3+3*x^4-3*x^6-2*x^7-x^8)/(1-x-x^2-x^3)^4.
MATHEMATICA
CoefficientList[Series[(1 - 2*x + x^2 + 4*x^3 + 3*x^4 - 3*x^6 - 2*x^7 - x^8)/(1 - x - x^2 - x^3)^4, {x, 0, 30}], x] (* Amiram Eldar, Feb 15 2024 *)
CROSSREFS
Cf. A370304.
Sequence in context: A258341 A054128 A082047 * A341803 A375273 A272483
KEYWORD
nonn,easy
AUTHOR
Jang Soo Kim, Feb 14 2024
STATUS
approved