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Search: id:A114582
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| A114582 |
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Number of Motzkin paths of length n having no UDH's starting at level 0 (U=(1,1),H=(1,0),D=(1,-1)). |
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+0
2
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| 1, 1, 2, 3, 7, 16, 40, 100, 256, 663, 1741, 4620, 12376, 33416, 90853, 248515, 683429, 1888449, 5240509, 14598709, 40810390, 114447429, 321885675, 907723460, 2566079622, 7270598910, 20643413513, 58727234739, 167373377361
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OFFSET
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0,3
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COMMENT
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Column 0 of A114581.
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FORMULA
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G.f.=2/[1-z+2z^3+sqrt(1-2z-3z^2)].
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EXAMPLE
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a(3)=3 because we have HHH, HUD, UHD, where U=(1,1),H=(1,0),D=(1,-1).
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MAPLE
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G:=2/(1-z+2*z^3+sqrt(1-2*z-3*z^2)): Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..32);
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CROSSREFS
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Cf. A114581.
Sequence in context: A049956 A081207 A027118 this_sequence A091487 A143884 A122031
Adjacent sequences: A114579 A114580 A114581 this_sequence A114583 A114584 A114585
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 09 2005
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