0,4

Nonisomorphic closed meanders, where two closed meanders are considered equivalent if one can be obtained from the other by reflections in an East-West mirror (a group of order 2).

A meander can be specified by marking 2n equally spaced points along a line and recording the order in which the meander visits the points.

For n = 2, 4, 6, 8 the solutions are as follows:

n=2: 1 2

n=4: 1 2 3 4

n=6: 1 2 3 4 5 6, 1 2 3 6 5 4, 1 2 5 4 3 6, 1 4 3 2 5 6

n=8: 1 2 3 4 5 6 7 8, 1 2 3 4 5 8 7 6, 1 2 3 4 7 6 5 8, 1 2 7 6 3 4 5 8, 1 2 3 6 7 8 5 4, 1 2 3 6 5 4 7 8,

n=8 (cont.): 1 2 5 4 3 6 7 8, 1 2 3 8 7 6 5 4, 1 2 5 4 3 8 7 6, 1 2 7 6 5 4 3 8, 1 2 3 8 5 6 7 4, 1 2 3 8 7 4 5 6, 1 2 5 6 7 4 3 8,

n=8 (cont.): 1 2 7 4 5 6 3 8, 1 4 3 2 5 6 7 8, 1 4 5 6 3 2 7 8, 1 4 3 2 5 8 7 6, 1 4 3 2 7 6 5 8, 1 6 5 4 3 2 7 8, 1 6 5 2 3 4 7 8, 1 6 3 4 5 2 7 8,

The total number of closed meanders with 2n crossings is given in A005315. Cf. A077055, A078104, A078105, A077460 (same but with group of order 4).

Sequence in context: A111177 A141052 A058308 this_sequence A090366 A131965 A104982

Adjacent sequences: A078588 A078589 A078590 this_sequence A078592 A078593 A078594

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com) and Jon Wild (wild(AT)music.mcgill.ca), Dec 07 2002