This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322634 #5 Dec 22 2018 16:14:54 %S A322634 5,153,4537,133189,3891675,113415423,3299905647 %N A322634 Sum of attendance numbers of all histories of length 5*n in the Bizley-Duchon's club model, divided by 5. %C A322634 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. %C A322634 Banderier et al. show that the mean area is asymptotic to K*n^(3/2), with K=(1/2)*(15*Pi)^(1/2). %H A322634 Cyril Banderier, Bernhard Gittenberger, <a href="https://hal.inria.fr/hal-01184683">Analytic Combinatorics of Lattice Paths: Enumeration and Asymptotics for the Area.</a> 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. %H A322634 Cyril Banderier, Michael Wallner, <a href="https://arxiv.org/abs/1605.02967">Lattice paths of slope 2/5</a>, arXiv:1605.02967 [cs.DM], 10 May 2016. %e A322634 a(1) = (15 + 10)/5 = 5: %e A322634 Contributions of the A293946(1) = 2 attendance histories are %e A322634 0 (+2) 2 (+2) 4 (+2) 6 (-3) 3 (-3) 0 -> 2 + 4 + 6 + 3 = 15 %e A322634 0 (+2) 2 (+2) 4 (-3) 1 (+2) 3 (-3) 0 -> 2 + 4 + 1 + 3 = 10. %Y A322634 Cf. A060941, A293946. %K A322634 nonn,more %O A322634 1,1 %A A322634 _Hugo Pfoertner_, Dec 22 2018