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Search: id:A095980
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| A095980 |
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Number of UFU-free Motzkin paths of length n. |
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+0
1
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| 1, 1, 2, 4, 9, 20, 47, 112, 274, 679, 1708, 4341, 11143, 28831, 75135, 197013, 519447, 1376256, 3662327, 9784106, 26232033, 70558313, 190348160
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = number of Motzkin paths (A001006) of length n that contain no consecutive UFU.
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FORMULA
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G.f.: (1 - x - x^3 - (1 - 2*x - 3*x^2 + 2*x^3 - 2*x^4 + x^6)^(1/2))/(2*x^2*(1 - x + x^2))
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EXAMPLE
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a(5) = 20 because, of the 21 Motzkin paths of length 5, only UFUDD contains an occurrence of UFU.
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CROSSREFS
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Sequence in context: A035084 A058385 A058386 this_sequence A036619 A036620 A036721
Adjacent sequences: A095977 A095978 A095979 this_sequence A095981 A095982 A095983
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KEYWORD
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nonn
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AUTHOR
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David Callan (callan(AT)stat.wisc.edu), Jul 16 2004
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