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

Author

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

Keywords

• nonn
• nice

Comments

There is no constraint on touching any particular sector.

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

Examples

			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.
		

Links

• Anonymous, Illustration for a(3) = 1

Crossrefs

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