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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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
| D. Merlini, Generating functions for the area below some lattice paths
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FORMULA
| G.f.: (1-sqrt(1-2*t-3*t^2))/((1-3*t)^2*(1+t))
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MAPLE
| 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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MATHEMATICA
| Rest[CoefficientList[Series[(1-Sqrt[1-2x-3x^2])/((1-3x)^2 (1+x)), {x, 0, 30}], x]] (* From Harvey P. Dale, Oct 20 2011 *)
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CROSSREFS
| Sequence in context: A137747 A094256 A005023 * A192803 A052161 A080960
Adjacent sequences: A094888 A094889 A094890 * A094892 A094893 A094894
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KEYWORD
| nonn,easy
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AUTHOR
| Donatella Merlini (merlini(AT)dsi.unifi.it), Jun 16 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 16 2004
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