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Search: id:A134425
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| A134425 |
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Number of paths of length n in the first quadrant, starting at the origin and consisting of 2 kinds of upsteps U=(1,1) (U1 and U2), 3 kinds of flatsteps F=(1,0) (F1, F2, and F3), and 1 kind of downsteps D=(1,-1). |
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+0
2
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| 1, 5, 27, 151, 861, 4969, 28911, 169187, 994329, 5862925, 34658691, 205305423, 1218183669, 7238062641, 43055682327, 256365292443, 1527728176305, 9110460044821, 54362600841963, 324557242893191, 1938584147698701
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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See A134426 for the enumeration of these paths according to the ordinates of their endpoints.
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FORMULA
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G.f.=2/(1-7z+sqrt(1-6z+z^2)). G.f.=g/(1-2zg), where g is the g.f. of the little Schroder numbers 1,3,11,45,197,... (A001003).
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EXAMPLE
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a(2)=5 because we have F1, F2, F3, U1, and U2. a(3)=27 because we have 9 paths of shape FF, 2 paths of shape UD, 6 paths of shape FU, 6 paths of shape UF, and 4 paths of shape UU.
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MAPLE
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G:=2/(1-7*z+sqrt(1-6*z+z^2)): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n= 0..20);
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CROSSREFS
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Cf. A001003, A134426.
Sequence in context: A015535 A026292 A100193 this_sequence A083326 A083880 A098409
Adjacent sequences: A134422 A134423 A134424 this_sequence A134426 A134427 A134428
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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), Nov 05 2007
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