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A089380
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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)).
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1
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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; internal format)
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OFFSET
| 0,5
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FORMULA
| G.f.=2(1-z)/[1-2z+3z^2+(1-z)sqrt(1-2z-3z^2)].
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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.
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CROSSREFS
| Cf. A001006.
Sequence in context: A197055 A062026 A048495 * A180282 A081154 A002900
Adjacent sequences: A089377 A089378 A089379 * A089381 A089382 A089383
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 27 2003
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