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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.

%I A077055 #44 May 06 2019 06:14:49
%S A077055 1,1,1,2,3,8,13,42,72,273,475,1970,3506,15368,27888,126510,233809,
%T A077055 1086546,2039564,9652364,18360296,88172609,169610371,824506191,
%U A077055 1601297937,7865294687,15401847339,76331857094,150547538649,751981532942,1492452957398
%N 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.
%C A077055 Meander shapes. [_Stéphane Legendre_, Apr 09 2013]
%H A077055 N. J. A. Sloane, <a href="/A077055/b077055.txt">Table of n, a(n) for n = 0..42</a> [from Legendre, 2013]
%H A077055 CombOS - Combinatorial Object Server, <a href="http://combos.org/meander">Generate meanders and stamp foldings</a>
%H A077055 Stéphane Legendre, <a href="/A077055/a077055.pdf">Illustration of initial terms</a>
%H A077055 Stéphane Legendre, <a href="http://arxiv.org/abs/1302.2025">Foldings and Meanders</a>, arXiv preprint arXiv:1302.2025 [math.CO], 2013.
%H A077055 J. Sawada and R. Li, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i2p43">Stamp foldings, semi-meanders, and open meanders: fast generation algorithms</a>, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
%F A077055 For n even a(n) = (A005316(n)+A005316(n/2))/2 (this is A078592).
%F A077055 For n odd a(n) = (A005316(n)+2*A223096(floor(n/2)))/4. [_Stéphane Legendre_, Apr 09 2013]
%e A077055 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.
%Y A077055 Cf. A005316, A077460, A078592, A223096.
%K A077055 nonn,nice
%O A077055 0,4
%A A077055 _N. J. A. Sloane_ and _Jon Wild_, Nov 29 2002
%E A077055 More terms from the Sawada-Li paper from _Daniel Recoskie_, Jul 11 2012