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Number of multiplex juggling cards with n balls and capacity 2.
1

%I #33 Aug 01 2024 18:37:23

%S 1,2,7,17,41,91,195,403,812,1601,3102,5922,11165,20824,38477,70513,

%T 128287,231893,416751,745073,1325770,2348929,4145388,7289460,12775705,

%U 22322558,38892931,67585361,117157061,202623103,349685883,602273695,1035354584,1776690881

%N Number of multiplex juggling cards with n balls and capacity 2.

%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_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-5,0,3,1).

%F G.f.: (1-x+x^2+x^3)/(1-x-x^2)^3.

%t CoefficientList[Series[(1 - x + x^2 + x^3)/(1 - x - x^2)^3, {x, 0, 33}], x] (* _Amiram Eldar_, Feb 15 2024 *)

%t LinearRecurrence[{3,0,-5,0,3,1},{1,2,7,17,41,91},40] (* _Harvey P. Dale_, Aug 01 2024 *)

%Y Cf. A370306.

%K nonn,easy

%O 0,2

%A _Jang Soo Kim_, Feb 14 2024