The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300996 Total sum of half the difference between the area above and the area below the path, measured within the smallest enclosing rectangle based on the x-axis, in all Dyck paths of semilength n. 2
 0, 0, 0, 1, 6, 28, 122, 516, 2142, 8776, 35630, 143757, 577548, 2313400, 9246556, 36899291, 147073062, 585662952, 2330527172, 9268803248, 36847836764, 146441131058, 581850689938, 2311451765318, 9181309423676, 36466002547328, 144826879361752, 575173217031049 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..50 Wikipedia, Counting lattice paths FORMULA a(n) = Sum_{k = -floor((n-1)^2/4)..floor((n-1)^2/4)} k * A300953(n,k). EXAMPLE a(3) = (1/2) * (0 -2 +2 +2 +0) = 1:    .______.    |  /\  |______.______.______.    | /  \ | /\/\ | /\   |   /\ |______.    |/____\|/____\|/__\/\|/\/__\|/\/\/\|    |9 -9=0|5-7=-2|7 -5=2|7 -5=2|3 -3=0| CROSSREFS Cf. A002620, A057571, A300953. Sequence in context: A225417 A026851 A267689 * A181337 A002693 A289779 Adjacent sequences:  A300993 A300994 A300995 * A300997 A300998 A300999 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 17 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 22:08 EDT 2022. Contains 354122 sequences. (Running on oeis4.)