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Search: id:A110122
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| A110122 |
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Number of Delannoy paths of length n with no EE's crossing the line y=x (i.e. no two consecutive E steps from the line y=x+1 to the line y=x-1; a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1), and D=(1,1)). |
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+0
3
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| 1, 3, 12, 53, 247, 1192, 5897, 29723, 152020, 786733, 4111295, 21661168, 114925697, 613442227, 3291704108, 17745496453, 96062011319, 521943400056, 2845404909129, 15558847792747, 85311186002036, 468951179698653
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 of A110121.
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REFERENCES
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R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
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FORMULA
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G.f.=1/[(1-zR)^2-z], where R=1+zR+zR^2=[1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of the large Schroeder numbers (A006318).
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EXAMPLE
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a(2)=12 because, among the 13 (=A001850(2)) Delannoy paths of length 2, only NEEN has an EE crossing the line y=x.
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MAPLE
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R:=(1-z-sqrt(1-6*z+z^2))/2/z: G:=1/((1-z*R)^2-z): Gser:=series(G, z=0, 27): 1, seq(coeff(Gser, z^n), n=1..24);
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CROSSREFS
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Cf. A110121, A001850.
Sequence in context: A124202 A138269 A026781 this_sequence A060460 A120983 A124810
Adjacent sequences: A110119 A110120 A110121 this_sequence A110123 A110124 A110125
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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), Jul 13 2005
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