A223096 -id:A223096 - cp's OEIS frontend

A060206 Number of rotationally symmetric closed meanders of length 4n+2.

1, 2, 10, 66, 504, 4210, 37378, 346846, 3328188, 32786630, 329903058, 3377919260, 35095839848, 369192702554, 3925446804750, 42126805350798, 455792943581400, 4967158911871358, 54480174340453578, 600994488311709056, 6664356253639465480

Offset: 0

N. J. A. Sloane, Apr 10 2001

Closed meanders of other lengths do not have rotational symmetry. - Andrew Howroyd, Nov 24 2015

See A077460 for additional information on the symmetries of closed meanders.

R. Bacher, Meander algebras
Andrew Howroyd, Illustration of a(1) and a(2)

Cf. A000682, A005315, A077055, A077460, A223096.

Meander sequences in Bacher's paper: A060066, A060089, A060111, A060148, A060149, A060174, A060198.

A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];
a[n_] := A000682[[2n + 1]];
a /@ Range[0, 20] (* Jean-François Alcover, Sep 03 2019 *)

a(n) = A000682(2n + 1). - Andrew Howroyd, Nov 24 2015

Name edited by Andrew Howroyd, Nov 24 2015

a(7)-a(20) from Andrew Howroyd, Nov 24 2015

A077055 Call two meanders from A005316 equivalent if they differ by a reflection in the Y axis (if n even) or by reflections in the X or Y axes (if n odd). Sequence gives number of inequivalent meanders with n crossings.

Original entry on oeis.org

1, 1, 1, 2, 3, 8, 13, 42, 72, 273, 475, 1970, 3506, 15368, 27888, 126510, 233809, 1086546, 2039564, 9652364, 18360296, 88172609, 169610371, 824506191, 1601297937, 7865294687, 15401847339, 76331857094, 150547538649, 751981532942, 1492452957398

Offset: 0

N. J. A. Sloane and Jon Wild, Nov 29 2002

Meander shapes. [Stéphane Legendre, Apr 09 2013]

			For n=7 the A005316(7) = 42 meanders with 7 crossings fall into 5 equivalence classes of size 2 and 8 of size 4, so a(7) = 5+8 = 13.

N. J. A. Sloane, Table of n, a(n) for n = 0..42 [from Legendre, 2013]
CombOS - Combinatorial Object Server, Generate meanders and stamp foldings
Stéphane Legendre, Illustration of initial terms
Stéphane Legendre, Foldings and Meanders, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
J. Sawada and R. Li, Stamp foldings, semi-meanders, and open meanders: fast generation algorithms, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).

Cf. A005316, A077460, A078592, A223096.

For n even a(n) = (A005316(n)+A005316(n/2))/2 (this is A078592).

For n odd a(n) = (A005316(n)+2*A223096(floor(n/2)))/4. [Stéphane Legendre, Apr 09 2013]

More terms from the Sawada-Li paper from Daniel Recoskie, Jul 11 2012

cp's OEIS Frontend

A060206 Number of rotationally symmetric closed meanders of length 4n+2.

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