A223093 -id:A223093 - cp's OEIS frontend

A217310 The number of meandering curves of order n, with only one extremity covered by its arcs.

0, 0, 4, 4, 32, 38, 264, 342, 2288, 3134, 20740, 29526, 194916, 285458, 1885840, 2822310, 18682016, 28440970, 188717116, 291294678, 1937706144, 3025232480, 20173268632, 31797822936, 212530874156, 337731551446, 2262235585956, 3620119437762, 24297593488468

Offset: 1

Panayotis Vlamos, Antonios Panayotopoulos, Georgia Theocharopoulou, Mar 17 2013

nonn

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

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

Panayotis Vlamos, Table of n, a(n) for n = 1..42
A. Panayotopoulos, P. Vlamos, Partitioning the Meandering Curves, Mathematics in Computer Science (2015) p 1-10.

Cf. A005315.

a(n) = A223093(n) * A000034(n). - Andrew Howroyd, Dec 06 2015

A223095 Number of foldings of n labeled stamps in which both end leaves are inwards.

Original entry on oeis.org

0, 0, 0, 2, 10, 40, 156, 546, 1986, 6716, 23742, 79472, 277178, 925588, 3205896, 10711486, 36963722, 123712788, 426075994, 1429030624, 4916833424, 16526958144, 56840484232, 191466923584, 658460090994, 2222507917328, 7644360501390, 25850724646008, 88938175307354

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

Cf. A000136, A000682, A077014.

Cf. A223093, A223094.

A217318 = Import["https://oeis.org/A217318/b217318.txt", "Table"][[All, 2]];
a[n_] := (2 - Mod[n, 2]) A217318[[n]];
Array[a, 42] (* Jean-François Alcover, Sep 02 2019 *)

a(n) = A223094(n) - A223093(n). - Andrew Howroyd, Dec 06 2015
a(n) = A000136(n) + A077014(n) - 2 * A000682(n). - Andrew Howroyd, Dec 06 2015
A217318(n) = a(n) if n is odd and A217318(n) = (1/2)*a(n) if n is even. - Stéphane Legendre, Jan 13 2014

Name clarified by Stéphane Legendre, Apr 09 2013

More terms from Stéphane Legendre, Apr 09 2013

cp's OEIS Frontend

A217310 The number of meandering curves of order n, with only one extremity covered by its arcs.

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