A227167 - OEIS

%I #28 Sep 20 2019 21:41:34

%S 1,1,6,8,50,72,462,696,4536,7030,46310,73188,485914,778946,5202690,

%T 8430992,56579196,92470194,622945970,1025114180,6927964218,

%U 11465054942,77692142980,129180293184,877395996200,1464716085664,9968202968958,16698145444260,113837957337750,191264779292430

%N The number of meandering curves of order n.

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

%C 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).

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

%H Jean-François Alcover, <a href="/A227167/b227167.txt">Table of n, a(n) for n = 1..45</a>

%H J. E. Koehler, <a href="http://dx.doi.org/10.1016/S0021-9800(68)80048-1">Folding a strip of stamps</a>, J. Combin. Theory, 5 (1968), 135-152.

%H W. F. Lunnon, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0221957-8">A map-folding problem</a>, Math. Comp. 22 (1968), 193-199.

%H A. Panayotopoulos, P. Vlamos, <a href="http://dx.doi.org/10.1007/s11786-015-0234-0">Partitioning the Meandering Curves</a>, Mathematics in Computer Science (2015) p 1-10.

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

%F a(n) = A217310(n) + A217318(n) + A005316(n). - _Andrew Howroyd_, Dec 07 2015

%t A000136 = Cases[Import["https://oeis.org/A000136/b000136.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := If[OddQ[n], A000136[[n]], A000136[[n]]/2];

%t a /@ Range[1, 45] (* _Jean-François Alcover_, Sep 20 2019 *)

%K nonn

%O 1,3

%A _Antonios Panayotopoulos_, _Panayotis Vlamos_, Jul 03 2013