A078105 Number of nonisomorphic ways a loop can cross three roads meeting in a Y n times (orbits under symmetry group of order 6).

1, 0, 1, 1, 2, 1, 8, 8, 48, 54, 331, 439, 2558, 3734, 21057, 33384, 182293, 307719, 1638465, 2913775, 15181584, 28194412, 144206012, 277887666, 1398566992

Offset

0,5

Comments

There is no constraint on touching any particular sector.

The Mercedes-Benz problem: closed meanders crossing a Y.

Links

Table of n, a(n) for n=0..24.

Anonymous, Illustration for a(3) = 1

Example

With three crossings the loop must cut each road exactly once, so a(3) = 1.
With 4 crossings the loop can cut one road 4 times (one possibility), or two roads twice each (one possibility), so a(4) = 2.

Crossrefs

Cf. A078104 (total number of solutions), A077460 and A005315 (loop crossing one road).

Sequence in context: A086657 A188922 A036296 * A075513 A284211 A246403

Adjacent sequences: A078102 A078103 A078104 * A078106 A078107 A078108

Keyword

nonn,nice

Author

N. J. A. Sloane and Jon Wild, Dec 05 2002

Status

approved