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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

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