A227167 The number of meandering curves of order n.

1, 1, 6, 8, 50, 72, 462, 696, 4536, 7030, 46310, 73188, 485914, 778946, 5202690, 8430992, 56579196, 92470194, 622945970, 1025114180, 6927964218, 11465054942, 77692142980, 129180293184, 877395996200, 1464716085664, 9968202968958, 16698145444260, 113837957337750, 191264779292430

Offset: 1

Author

Antonios Panayotopoulos, Panayotis Vlamos, Jul 03 2013

Keywords

• nonn

Comments

A meandering curve of order n is a continuous curve which does not intersect itself yet intersects a horizontal line n times.

The set of meandering curves of order n is partitioned into the following three classes: curves with no extremities (A005316), curves with only one extremity (A217310), and curves with both extremities covered by their arcs (A217318).

References

• A. Panayotopoulos and P. Tsikouras, Properties of meanders, JCMCC 46 (2003), 181-190.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..45
• J. E. Koehler, Folding a strip of stamps, J. Combin. Theory, 5 (1968), 135-152.
• W. F. Lunnon, A map-folding problem, Math. Comp. 22 (1968), 193-199.
• A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10.

Programs

Mathematica

A000136 = Cases[Import["https://oeis.org/A000136/b000136.txt", "Table"], {, }][[All, 2]];
a[n_] := If[OddQ[n], A000136[[n]], A000136[[n]]/2];
a /@ Range[1, 45] (* Jean-François Alcover, Sep 20 2019 *)

Formula

a(n) = A000136(n) if n is odd and a(n) = (1/2)*A000136(n) if n is even.

a(n) = A217310(n) + A217318(n) + A005316(n). - Andrew Howroyd, Dec 07 2015