A217310 -id:A217310 - cp's OEIS frontend

A223093 Number of foldings of n labeled stamps in which leaf 1 is inwards and leaf n outwards (or leaf 1 outwards and leaf n inwards).

0, 0, 2, 4, 16, 38, 132, 342, 1144, 3134, 10370, 29526, 97458, 285458, 942920, 2822310, 9341008, 28440970, 94358558, 291294678, 968853072, 3025232480, 10086634316, 31797822936, 106265437078, 337731551446, 1131117792978, 3620119437762, 12148796744234, 39118879440938

Offset: 1

N. J. A. Sloane, Mar 29 2013

nonn

Subset of foldings of n labeled stamps (A000136). - Stéphane Legendre, Apr 09 2013

Stéphane Legendre, Table of n, a(n) for n = 1..42
S. Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
S. Legendre, Foldings and Meanders, Aust. J. Comb. 58(2), 275-291, 2014.
Index entries for sequences obtained by enumerating foldings

A000682 = Cases[Import["https://oeis.org/A000682/b000682.txt", "Table"], {, }][[All, 2]];
A077014 = Cases[Import["https://oeis.org/A077014/b077014.txt", "Table"], {, }][[All, 2]];
a[n_] := A000682[[n + 1]] - A077014[[n + 1]];
Array[a, 30] (* Jean-François Alcover, Sep 07 2019, after Andrew Howroyd *)

a(n) = A000682(n+1) - A077014(n). - Andrew Howroyd, Dec 06 2015

A217310(n) = 2*a(n) if n is odd and A217310(n) = a(n) if n is even. - Stéphane Legendre, Jan 09 2014

Name clarified by Stéphane Legendre, Apr 09 2013

More terms from Stéphane Legendre, Apr 09 2013

A227167 The number of meandering curves of order n.

Original entry on oeis.org

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

Antonios Panayotopoulos, Panayotis Vlamos, Jul 03 2013

nonn

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).

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

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.

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 *)

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

cp's OEIS Frontend

A223093 Number of foldings of n labeled stamps in which leaf 1 is inwards and leaf n outwards (or leaf 1 outwards and leaf n inwards).

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