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Search: id:A109190
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| A109190 |
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Number of (1,0)-steps at level zero in all Grand Motzkin paths of length n. (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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+0
2
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| 1, 0, 2, 2, 8, 16, 46, 114, 310, 822, 2238, 6094, 16764, 46308, 128650, 358862, 1005056, 2824416, 7962122, 22508350, 63792424, 181219680, 515905018, 1471593638, 4205280902, 12037415526, 34510499066, 99083855234, 284870069780
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OFFSET
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0,3
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COMMENT
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Column 0 of A109189.
The substitution x->x/(1+x+x^2) in the g.f. (this might be called an inverse Motzkin transform), yields the g.f. of (-1)^n*A006355(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2008]
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FORMULA
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G.f.=[sqrt(1-2z-3z^2)-z]/(1-2z-4z^2).
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EXAMPLE
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a(3)=2 because we have uhd and dhu.
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MAPLE
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g:=(sqrt(1-2*z-3*z^2)-z)/(1-2*z-4*z^2): gser:=series(g, z=0, 33): 1, seq(coeff(gser, z^n), n=1..30);
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CROSSREFS
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Cf. A109189.
Sequence in context: A026585 A098273 A052970 this_sequence A016120 A085542 A009725
Adjacent sequences: A109187 A109188 A109189 this_sequence A109191 A109192 A109193
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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), Jun 21 2005
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