A391919 - OEIS

%I #27 Feb 05 2026 16:52:31

%S 1,1,1,1,4,1,2,7,14,1,3,24,36,48,1,8,47,188,166,166,1,14,168,459,1224,

%T 730,584,1,42,352,2112,3601,7202,3138,2092,1,81,1296,5166,20664,24880,

%U 39808,13328,7616,1,262,2851,22808,57888,173664,158244,210992,56204,28102,1

%N Triangle read by rows: T(n, k) is the number of singular meanders with n intersections having k tangential intersections.

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

%H Yury Belousov, <a href="/A391919/b391919.txt">Rows n = 0..19 of triangle, flattened</a>.

%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.

%e Triangle begins:

%e   1;

%e   1,  1;

%e   1,  4,  1;

%e   2,  7, 14,  1;

%e   3, 24, 36, 48, 1;

%e   ...

%Y Column 0 is A005316.

%Y Main diagonal gives A000012.

%Y Subdiagonal gives A082590.

%Y Row sums give A393122.

%K nonn,tabl,hard

%O 0,5

%A _Yury Belousov_, Jan 27 2026