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Search: id:A035011
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| 0, 1, 5, 21, 89, 393, 1805, 8557, 41585, 206097, 1037717, 5293445, 27297737, 142078745, 745387037, 3937603037, 20927156705, 111818026017, 600318853925, 3236724317173
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OFFSET
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0,3
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COMMENT
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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
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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
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Cf. A006318.
Sequence in context: A010917 A015448 A099843 this_sequence A113987 A164037 A125784
Adjacent sequences: A035008 A035009 A035010 this_sequence A035012 A035013 A035014
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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