A078104 Number of ways a loop can cross three roads meeting in a Y n times. The loop must touch the southwest sector.

1, 0, 2, 1, 7, 6, 37, 42, 237, 320, 1715, 2610, 13478, 22404, 112480, 200158, 982561, 1846314, 8897089, 17481864

Offset: 0

Author

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

Keywords

• nonn

Comments

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 (giving A005315(2)*2 = 4 possibilities), or two roads twice each (3 ways), so a(4) = 7.
		

Links

• Anonymous, Illustration for a(3) = 1

Crossrefs

See A085919 for another version. Cf. A078105 (nonisomorphic solutions), A077460 and A005315 (loop crossing one road).

Cf. also A077550.

Extensions

More terms added Aug 25 2003