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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
OFFSET
0,3
FORMULA
G.f.: (1-z)(1-z-q)/(z(3-3z-q)), where q = sqrt(1-6z+z^2).
D-finite with recurrence 2*(n+1)*a(n) +(-17*n+7)*a(n-1) +(37*n-59)*a(n-2) +(-37*n+89)*a(n-3) +(17*n-61)*a(n-4) +2*(-n+5)*a(n-5)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
Example: a(2)=2 because we have HH and UUDD.
CROSSREFS
Cf. A006318.
Sequence in context: A027743 A152124 A147722 * A206902 A275752 A084868
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 28 2003
STATUS
approved