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A076876
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Meandric numbers for a river crossing two parallel roads at n points.
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6
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1, 1, 2, 3, 8, 14, 43, 81, 272, 538, 1920, 3926
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = number of ways that a curve can start in the (-,-) quadrant, cross two parallel lines and end up in the (+,+) or (+,-) quadrant if n is even or head East between the two roads if n is odd.
A107321 is a lower bound. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
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LINKS
| R. J. Mathar, ASCII representations
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EXAMPLE
| Let b(n) = A005316(n). Then a(0) = b(0), a(1) = b(1), a(2) = b(1) + b(2), a(3) = b(3) + b(2), a(4) = b(4) + 2*b(3) + 1, a(5) = b(5) + b(3)*b(2) + b(4) + 1.
Consider n=5: if we do not cross the second road there are b(5) = 8 solutions. If we cross the first road 3 times and then the second road twice there are b(3)*b(2) = 2 solutions. If we cross the first road once and the second road 4 times there are b(4) = 3 solutions. The only other possibility is to cross road 1, road 2 twice, road 1 twice and exit to the right.
For larger n it is convenient to give the vector of the number of times the same road is crossed. For example for n=6 the vectors and the numbers of possibilities are as follows:
[6] ...... 14
[5 1] ..... 8
[3 3] ..... 4
[3 2 1] ... 2
[1 5] ..... 8
[1 4 1] ... 3
[1 2 3] ... 2
[1 2 2 1] . 2
Total .... 43
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CROSSREFS
| Cf. A005316, A076875, A076906, A076907.
Sequence in context: A007165 A107321 A005316 * A124495 A007919 A205101
Adjacent sequences: A076873 A076874 A076875 * A076877 A076878 A076879
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KEYWORD
| nonn,more,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Jon Wild (wild(AT)music.mcgill.ca), Nov 26, 2002
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 04 2007
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