id:A089387 - OEIS Search Results

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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.

+0
2

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; listen)

	OFFSET	`0,3`
	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 this_sequence A084868 A109980 A110837` `Adjacent sequences: A089384 A089385 A089386 this_sequence A089388 A089389 A089390`
	KEYWORD	`nonn`
	AUTHOR	`Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003`

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.

AT&T Labs Research