OFFSET
1,1
COMMENTS
The Bizley-Duchon's club model is equivalent to the lattice paths from (0,0) to (3*n,2*n) described in A293946. The attendance history of the club consists of persons entering in pairs and leaving in groups of three. The club closes when no persons are remaining. a(k)/A293946(k) is proportional to the mean area under the "filling level curve" of the club.
Banderier et al. show that the mean area is asymptotic to K*n^(3/2), with K=(1/2)*(15*Pi)^(1/2).
LINKS
Cyril Banderier, Bernhard Gittenberger, Analytic Combinatorics of Lattice Paths: Enumeration and Asymptotics for the Area. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.345-356, 2006, DMTCS Proceedings.
Cyril Banderier, Michael Wallner, Lattice paths of slope 2/5, arXiv:1605.02967 [cs.DM], 10 May 2016.
EXAMPLE
a(1) = (15 + 10)/5 = 5:
Contributions of the A293946(1) = 2 attendance histories are
0 (+2) 2 (+2) 4 (+2) 6 (-3) 3 (-3) 0 -> 2 + 4 + 6 + 3 = 15
0 (+2) 2 (+2) 4 (-3) 1 (+2) 3 (-3) 0 -> 2 + 4 + 1 + 3 = 10.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner, Dec 22 2018
STATUS
approved