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Number of multiplex juggling cards with n balls and capacity 3.
1

%I #29 Feb 16 2024 12:05:34

%S 1,2,7,24,70,198,532,1370,3418,8296,19677,45770,104687,235972,525136,

%T 1155516,2517199,5434454,11638099,24741812,52250956,109678746,

%U 228948036,475479494,982831024,2022696684,4145947065,8466032502,17226979885,34939008232,70643799296,142423352600

%N Number of multiplex juggling cards with n balls and capacity 3.

%H S. Butler, J. Choi, K. Kim, and K. Seo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Butler/butler12.html">Enumerating multiplex juggling patterns</a>, J. Integer Seq., 22(1):Art. 19.1.7, 21, 2019.

%H Y. Cho, J. Kim, J. S. Kim, and N. Lee, <a href="https://arxiv.org/abs/2402.09903">Enumeration of multiplex juggling card sequences using generalized q-derivatives</a>, arXiv:2402.09903 [math.CO], 2014.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-4,-7,8,12,8,-7,-12,-10,-4,-1).

%F 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.

%t 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 *)

%Y Cf. A370304.

%K nonn,easy

%O 0,2

%A _Jang Soo Kim_, Feb 14 2024