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

1,3

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.

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

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 *)

Crossrefs

Sequence in context: A154153 A164640 A223852 * A192158 A167481 A137122

Adjacent sequences: A227164 A227165 A227166 * A227168 A227169 A227170

Keyword

nonn

Author

Antonios Panayotopoulos, Panayotis Vlamos, Jul 03 2013

Status

approved