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Search: id:A134424
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| A134424 |
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Area under all paths in the first quadrant from (0,0) to (n,0) using steps U=(1,1), D=(1,-1), h=(1,0), and H=(2,0). |
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+0
2
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| 0, 0, 1, 4, 21, 80, 316, 1152, 4186, 14812, 52020, 180616, 623338, 2138040, 7302035, 24842736, 84262609, 285052676, 962184359, 3241616628, 10903119167, 36619715860, 122837641530, 411588875136, 1377735161776, 4607695277512
(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)=Sum(k*A134423(n,k),k>=0).
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FORMULA
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G.f.=z^2(1+z^2)g^2/[(1+z-z^2)(1-3z-z^2), where g=1+zg+z^2g+z^2g^2 (g is the g.f. of A128720).
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EXAMPLE
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a(3)=4 because the areas under the paths hhh, hH, Hh, hUD, UhD, and UDh are 0,0,0,1,2, and 1, respectively.
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MAPLE
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g:=((1-z-z^2-sqrt((1+z-z^2)*(1-3*z-z^2)))*1/2)/z^2: G:=z^2*(1+z^2)*g^2/((1+z-z^2)*(1-3*z-z^2)): Gser:=series(G, z=0, 32): seq(coeff(Gser, z, n), n=0..25);
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CROSSREFS
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Cf. A128720, A134423.
Sequence in context: A078800 A057333 A034960 this_sequence A017967 A076901 A080043
Adjacent sequences: A134421 A134422 A134423 this_sequence A134425 A134426 A134427
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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), Oct 25 2007
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