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

0,3

Comments

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

Links

Table of n, a(n) for n=0..19.

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

Crossrefs

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

Cf. also A077550.

Sequence in context: A060583 A246751 A295850 * A072280 A217106 A329995

Adjacent sequences: A078101 A078102 A078103 * A078105 A078106 A078107

Keyword

nonn

Author

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

Extensions

More terms added Aug 25 2003

Status

approved