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A078105
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Number of nonisomorphic ways a loop can cross three roads meeting in a Y n times (orbits under symmetry group of order 6).
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| There is no constraint on touching any particular sector.
The Mercedes-Benz problem: closed meanders crossing a Y.
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LINKS
| Anonymous, Illustration for a(3) = 1
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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.
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CROSSREFS
| Cf. A078104 (total number of solutions), A077460 and A005315 (loop crossing one road).
Sequence in context: A086657 A188922 A036296 * A075513 A011019 A193728
Adjacent sequences: A078102 A078103 A078104 * A078106 A078107 A078108
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Jon Wild (wild(AT)music.mcgill.ca), Dec 05 2002
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