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A370304
Number of multiplex juggling cards with n balls and capacity 2.
1
1, 2, 7, 17, 41, 91, 195, 403, 812, 1601, 3102, 5922, 11165, 20824, 38477, 70513, 128287, 231893, 416751, 745073, 1325770, 2348929, 4145388, 7289460, 12775705, 22322558, 38892931, 67585361, 117157061, 202623103, 349685883, 602273695, 1035354584, 1776690881
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.
FORMULA
G.f.: (1-x+x^2+x^3)/(1-x-x^2)^3.
MATHEMATICA
CoefficientList[Series[(1 - x + x^2 + x^3)/(1 - x - x^2)^3, {x, 0, 33}], x] (* Amiram Eldar, Feb 15 2024 *)
LinearRecurrence[{3, 0, -5, 0, 3, 1}, {1, 2, 7, 17, 41, 91}, 40] (* Harvey P. Dale, Aug 01 2024 *)
CROSSREFS
Cf. A370306.
Sequence in context: A175660 A365069 A347079 * A375821 A175120 A239357
KEYWORD
nonn,easy
AUTHOR
Jang Soo Kim, Feb 14 2024
STATUS
approved