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Search: id:A104545
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| A104545 |
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Number of Motzkin paths of length n having no consecutive (1,0) steps. |
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+0
2
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| 1, 1, 1, 3, 5, 11, 25, 55, 129, 303, 721, 1743, 4241, 10415, 25761, 64095, 160385, 403263, 1018369, 2581887, 6569089, 16767871, 42927105, 110194175, 283574017, 731427583, 1890600193, 4896499455, 12704869633, 33021750015, 85966113281
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=A104544(n,0) (n>0).
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FORMULA
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G.f.=[1-sqrt(1-4z^2*(1+z)^2)]/[2z^2*(1+z)].
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EXAMPLE
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a(3)=3 because we have UDH, HUD, and UHD, where U=(1,1), D=(1,-1), and H=(1,0) (HHH does not qualify).
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MAPLE
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G:=(1-sqrt(1-4*z^2*(1+z)^2))/2/z^2/(1+z): Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..31);
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CROSSREFS
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Cf. A001006, A104544.
Adjacent sequences: A104542 A104543 A104544 this_sequence A104546 A104547 A104548
Sequence in context: A076051 A018116 A018008 this_sequence A027050 A109249 A032364
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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), Mar 14 2005
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