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 A368164 #19 Jul 07 2024 13:15:29
%S A368164 1,7,63,583,5407,50007,460815,4231815,38745279,353832631,3224323183,
%T A368164 29328492519,266364307231,2416023142423,21890268365007,
%U A368164 198151683934023,1792260214473087,16199857938091383,146342491104098607,1321339563995562663,11925412051760977887,107590261672922633943
%N A368164 Number of nondeterministic Dyck bridges of length 2*n.
%C A368164 In nondeterministic walks (N-walks) the steps are sets and called N-steps. N-walks start at 0 and are concatenations of such N-steps such that all possible extensions are explored in parallel. The nondeterministic Dyck step set is { {-1}, {1}, {-1,1} }. Such an N-walk is called an N-bridge if it contains at least one trajectory that is a classical bridge, i.e., starts and ends at 0 (for more details see the de Panafieu-Wallner article).
%H A368164 Élie de Panafieu and Michael Wallner, <a href="https://arxiv.org/abs/2311.03234">Combinatorics of nondeterministic walks</a>, arXiv:2311.03234 [math.CO], 2023.
%F A368164 G.f.: (1-6*t)/(sqrt(1-8*t)*(1-9*t)).
%F A368164 From _Joseph M. Shunia_, May 09 2024: (Start)
%F A368164 a(n) = A089022(n) + Sum_{k=0..n-1} binomial(2*n, k)*2^(2*n-k).
%F A368164 a(n) = A000244(2*n) - Sum_{k=n+1..2*n} binomial(2*n, k)*2^(2*n-k+1). (End)
%e A368164 The a(1)=7 N-bridges of length 2 are
%e A368164 / / /
%e A368164 /\, , /\, , /\, / , /\
%e A368164 \/ \/ \ \/ \/
%e A368164 \ \ \
%Y A368164 Cf. A151281 (nondeterministic Dyck meanders), A368234 (nondeterministic Dyck excursions), A000244 (nondeterministic Dyck walks).
%K A368164 nonn
%O A368164 0,2
%A A368164 _Michael Wallner_, Dec 14 2023