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Search: id:A094891
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| A094891 |
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Total area below the lattice paths of a given length defined by the rule [(0),(k)->(k-1)(k)(k+1)] (Motzkin paths). |
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+0
1
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| 1, 7, 34, 144, 563, 2095, 7532, 26410, 90853, 307893, 1030886, 3417450, 11235151, 36676453, 119003432, 384098710, 1234016321, 3948461521, 12588083810, 40001960362, 126745795259, 400532044957, 1262690290868, 3971944688584
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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D. Merlini, Generating functions for the area below some lattice paths, Discrete Mathematics and Theoretical Computer Science AC, 2003, 217-228.
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LINKS
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D. Merlini, Generating functions for the area below some lattice paths
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FORMULA
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G.f.: (1-sqrt(1-2*t-3*t^2))/((1-3*t)^2*(1+t))
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MAPLE
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G:=(1-sqrt(1-2*t-3*t^2))/((1-3*t)^2*(1+t)): Gser:=series(G, t=0, 30): seq(coeff(Gser, t^n), n=1..28); (Deutsch)
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CROSSREFS
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Sequence in context: A137747 A005023 A094256 this_sequence A052161 A080960 A099242
Adjacent sequences: A094888 A094889 A094890 this_sequence A094892 A094893 A094894
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KEYWORD
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nonn,easy
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AUTHOR
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Donatella Merlini (merlini(AT)dsi.unifi.it), Jun 16 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 16 2004
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