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A298122 a(n) is the number of n nonintersecting arches above the x-axis that start and/or end with an arch length equal to one and have floor((n+2)/2) arches starting in odd numbered positions. 0
1, 1, 2, 5, 11, 34, 90, 300, 875, 3038, 9408, 33516, 108108, 392040, 1302444, 4785066, 16256955, 60324550, 208579800, 780088452, 2735682092, 10296854984, 36532677272, 138231751840, 495241833996, 1882201158264, 6799413051200, 25939319270000, 94374970110000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..29.

FORMULA

a(1) = a(2) = 1, a(3) = 2; for n > 3, a(n) = 2*(C(n-1, floor((n-1)/2))*C(n-2, floor((n-2)/2)) - (C(n-1, floor((n-2)/2))*C(n-2, floor((n-3)/2)))) - (C(n-3, floor((n-1)/2))*C(n-2, floor((n-1)/2))/(floor((n-1)/2)+1)).

EXAMPLE

Example: For n = 4 the a(4) = 5 solutions are as follows. (The numbers under the arches represent arches starting in an odd-numbered position on the x-axis.)

    /\                                /\

   //\\      /\            /\        //\\        /\

  ///\\\/\, //\\ /\ /\, /\//\\/\, /\///\\\, /\/\//\\.

  1 3   7   1    5  7   1 3   7   1 3 5     1 3 5

CROSSREFS

Cf. A001263, A005558.

Sequence in context: A080068 A226919 A307316 * A196690 A101834 A117758

Adjacent sequences:  A298119 A298120 A298121 * A298123 A298124 A298125

KEYWORD

nonn

AUTHOR

Roger Ford, Jan 12 2018

STATUS

approved

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Last modified April 3 01:23 EDT 2020. Contains 333195 sequences. (Running on oeis4.)