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A114584
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Number of Motzkin paths of length n having no UHD's (U=(1,1),H=(1,0),D=(1,-1)).
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1
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1, 1, 2, 3, 7, 15, 36, 85, 209, 517, 1303, 3312, 8510, 22029, 57447, 150709, 397569, 1053822, 2805518, 7498035, 20110254, 54110386, 146021880, 395114304, 1071772322, 2913900196, 7939004648, 21672609566, 59272260791, 162380575451
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Column 0 of A114583.
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FORMULA
| G.f.=[1-z+z^3-sqrt((1+z+z^3)(1-3z+z^3)]/(2z^2).
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EXAMPLE
| a(4)=7 because the only counterexamples among the 9 Motzkin paths of length 4 are HUHD and UHDH.
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MAPLE
| G:=(1-z+z^3-sqrt((1+z+z^3)*(1-3*z+z^3)))/2/z^2: Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..32);
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CROSSREFS
| Cf. A114583.
Sequence in context: A005909 A003006 A052321 * A039826 A161746 A045629
Adjacent sequences: A114581 A114582 A114583 * A114585 A114586 A114587
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 09 2005
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