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.

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

0,4

Comments

Meander shapes. [Stéphane Legendre, Apr 09 2013]

Links

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).

Formula

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]

Example

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.

Crossrefs

Cf. A005316, A077460, A078592, A223096.

Sequence in context: A294566 A129873 A025575 * A327868 A145929 A153865

Adjacent sequences: A077052 A077053 A077054 * A077056 A077057 A077058

Keyword

nonn,nice

Author

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

Extensions

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

Status

approved