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A268370 Number of North-East lattice paths from (0,0) to (n,n) that have exactly three east steps below the subdiagonal y = x-1. 1
5, 24, 95, 356, 1309, 4784, 17472, 63920, 234498, 863056, 3187041, 11807740, 43885725, 163601760, 611625660, 2292665760, 8615485590, 32451382800, 122499978510, 463369822344, 1756113365874, 6667436894624, 25357090075600, 96589604043296, 368478056090340, 1407687015207200, 5384924914890213 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

This sequence is related to paired pattern P_1 in Pan and Remmel's link.

LINKS

Table of n, a(n) for n=4..30.

Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.

FORMULA

G.f.: -((-1 + f(x) + 2*x)^2*(-1 + f(x) + 2*(f(x) - 2*x)*x))/(8*x^2), where f(x) = sqrt(1 - 4*x).

CROSSREFS

Cf. A120989, A002057, A000108.

Sequence in context: A271458 A180354 A212349 * A087095 A099653 A270126

Adjacent sequences:  A268367 A268368 A268369 * A268371 A268372 A268373

KEYWORD

nonn

AUTHOR

Ran Pan, Feb 03 2016

STATUS

approved

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Last modified September 26 06:24 EDT 2017. Contains 292502 sequences.