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A095980 Number of UFU-free Motzkin paths of length n. 1
1, 1, 2, 4, 9, 20, 47, 112, 274, 679, 1708, 4341, 11143, 28831, 75135, 197013, 519447, 1376256, 3662327, 9784106, 26232033, 70558313, 190348160, 514904151, 1396328313, 3795324358, 10338000693, 28215285901, 77149545999, 211314835549, 579730469034 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = number of Motzkin paths (A001006) of length n that contain no consecutive UFU.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

FORMULA

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)).

EXAMPLE

a(5) = 20 because, of the 21 Motzkin paths of length 5, only UFUDD contains an occurrence of UFU.

PROG

(PARI) seq(n)={Vec((1 - x - x^3 - (1 - 2*x - 3*x^2 + 2*x^3 - 2*x^4 + x^6 + O(x^3*x^n))^(1/2))/(2*x^2*(1 - x + x^2)))} \\ Andrew Howroyd, Nov 05 2019

CROSSREFS

Cf. A001006.

Sequence in context: A213905 A058385 A058386 * A036619 A036620 A036721

Adjacent sequences:  A095977 A095978 A095979 * A095981 A095982 A095983

KEYWORD

nonn

AUTHOR

David Callan, Jul 16 2004

EXTENSIONS

Terms a(23) and beyond from Andrew Howroyd, Nov 05 2019

STATUS

approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)