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A089387 Number of Schroeder paths of semilength n (i.e., lattice paths from (0,0) to (2n,0), with steps H=(2,0), U=(1,1) and D(1,-1) and not going below the x-axis) with no UD, UHD, UHHD, UHHHD, ... starting at level zero. 1
1, 1, 2, 8, 36, 164, 764, 3652, 17852, 88868, 449004, 2296692, 11870316, 61897140, 325239036, 1720415268, 9154052700, 48961321604, 263092909004, 1419630359572, 7689097400588, 41788586179988, 227819374037340, 1245545102522948 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: (1-z)(1-z-q)/(z(3-3z-q)), where q = sqrt(1-6z+z^2).

EXAMPLE

Example: a(2)=2 because we have HH and UUDD.

CROSSREFS

Cf. A006318.

Sequence in context: A027743 A152124 A147722 * A206902 A275752 A084868

Adjacent sequences:  A089384 A089385 A089386 * A089388 A089389 A089390

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 28 2003

STATUS

approved

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Last modified September 22 17:13 EDT 2019. Contains 327311 sequences. (Running on oeis4.)