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 A089380 Number of Motzkin paths of length n with no UD, UHD, UHHD, UHHHD, ..., starting at level zero (here H=(1,0), U=(1,1), D=(1,-1)). 1
 1, 1, 1, 1, 2, 6, 18, 50, 133, 349, 919, 2443, 6559, 17759, 48417, 132765, 365883, 1012827, 2814975, 7852359, 21977172, 61697208, 173688720, 490222392, 1386896799, 3932313671, 11172152779, 31801604227, 90683754826, 259017103918 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA G.f.=2(1-z)/[1-2z+3z^2+(1-z)sqrt(1-2z-3z^2)]. EXAMPLE a(5)=6 because among the 21 Motzkin paths of length 5 only the following have no U(H^p)D for any p>=0: HHHHH, HUUDD, UUDDH, UHUDD, UUDHD and UUHDD. CROSSREFS Cf. A001006. Sequence in context: A258625 A062026 A048495 * A271897 A304962 A180282 Adjacent sequences:  A089377 A089378 A089379 * A089381 A089382 A089383 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 27 2003 STATUS approved

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Last modified April 11 01:52 EDT 2021. Contains 342886 sequences. (Running on oeis4.)