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Search: id:A104550
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| A104550 |
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Number of horizontal segments in all Schroeder paths of length 2n (a horizontal segment is a maximal string of horizontal steps). A Schroeder path is a lattice path starting from (0,0), ending at a point on the x-axis, consisting only of steps U=(1,1), D=(1,-1), and H=(2,0), and never going below the x-axis. Schroeder paths are counted by the large Schroeder numbers (A006318). |
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+0
2
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| 1, 4, 20, 104, 552, 2972, 16172, 88720, 489872, 2719028, 15157188, 84799992, 475894200, 2677788492, 15102309468, 85347160608, 483183316512, 2739851422820, 15558315261812, 88462135512712, 503569008273992
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.=(1-z)[1-z-sqrt(1-6z+z^2)]/[2sqrt(1-6z+z^2)]
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EXAMPLE
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a(2)=4 because we have (HH),(H)UD,UD(H),U(H)D,UDUD, and UUDD; the 4 horizontal segments are shown between parentheses.
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MAPLE
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G:=(1-z)*(1-z-sqrt(1-6*z+z^2))/2/sqrt(1-6*z+z^2): Gser:=series(G, z=0, 28): seq(coeff(Gser, z^n), n=1..24);
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CROSSREFS
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Cf. A006318, A104549.
Sequence in context: A076035 A120978 A035028 this_sequence A089382 A026305 A131786
Adjacent sequences: A104547 A104548 A104549 this_sequence A104551 A104552 A104553
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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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