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0, 1, 5, 21, 89, 393, 1805, 8557, 41585, 206097, 1037717, 5293445, 27297737, 142078745, 745387037, 3937603037, 20927156705, 111818026017, 600318853925, 3236724317173
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of occurrences of UD, UHD, UHHD, UHHHD, ... starting at level zero in all 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). Example: a(2) = 5 because in the six paths of semilength 2, namely HH, H(UD), (UD)H, (UHD), (UD)(UD), UUDD, we have 5 required occurrences (shown between parentheses). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
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FORMULA
| G.f.=(1-4z+z^2)/[2z(1-z)]-sqrt(1-6z+z^2)/(2z). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
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CROSSREFS
| Cf. A006318.
Sequence in context: A010917 A015448 A099843 * A113987 A188707 A164037
Adjacent sequences: A035008 A035009 A035010 * A035012 A035013 A035014
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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