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A109192
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Number of Grand Motzkin paths of length n and having no hills (i.e. no ud's starting at level 0).(A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).
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1
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1, 1, 2, 5, 13, 34, 91, 247, 678, 1877, 5233, 14674, 41349, 117001, 332260, 946527, 2703915, 7743268, 22223607, 63909987, 184121946, 531318553, 1535522513, 4443815554, 12876794147, 37356832679, 108494114718, 315415738025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Column 0 of A109191.
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FORMULA
| G.f.=1/[z^2+sqrt(1-2z-3z^2)].
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EXAMPLE
| a(3)=5 because we have hhh,hdu,duh,uhd and dhu.
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MAPLE
| g:=1/(z^2+sqrt(1-2*z-3*z^2)): gser:=series(g, z=0, 33): 1, seq(coeff(gser, z^n), n=1..31);
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CROSSREFS
| Cf. A109191.
Sequence in context: A114173 A023425 A090827 * A192313 A193039 A062465
Adjacent sequences: A109189 A109190 A109191 * A109193 A109194 A109195
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2005
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