A393122 - OEIS

%I #10 Feb 08 2026 16:56:09

%S 1,2,6,24,112,576,3180,18540,112840,711016,4610036,30614932,207498060,

%T 1431260984,10024424284,71158769844,511160782120,3710968813976,

%U 27198487483336,201060296071624,1497907249045496,11238798692083888

%N Number of singular meanders with n intersections.

%C Singular meanders are a generalization of standard (open) meanders (A005316) allowing tangential intersections.

%H Yury Belousov, <a href="http://ftp.pdmi.ras.ru/pub/publicat/znsl/v549/p049.pdf">Singular meanders</a>, Zap. Nauchn. Sem. POMI, 549 (2025), 49-64.

%H Yury Belousov, <a href="https://arxiv.org/abs/2112.10289">Prime Factorization of Meanders</a>, arXiv:2112.10289 [math.CO], 2025.

%H Yury Belousov, <a href="https://github.com/YuryBelousov/meander_factorization">C++ code for generating the sequence</a>, GitHub.

%F a(n) = Sum_{k=0..n} A391919(n, k).

%e For n = 1, a(1) = 2. There are 2 singular meanders with a single intersection: one with a transverse intersection and one with a tangential intersection.

%Y Row sums of triangle A391919.

%K nonn,hard,more

%O 0,2

%A _Yury Belousov_, Feb 02 2026