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A286760 Total number of nodes summed over all lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y and consist of steps U=(1,1), D=(1,-1), H=(1,0) and S=(0,1). 2
1, 2, 10, 42, 214, 1098, 5978, 33190, 189078, 1093490, 6414714, 38027030, 227489950, 1370980490, 8314674202, 50696630838, 310541818382, 1909850054666, 11786947172234, 72969941803662, 452976340653030, 2818815920369754, 17579546535174946, 109850944544149134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ c * (3 + 2*sqrt(3))^n / sqrt(n), where c = 0.0889843039487036085233000284915570190371055498671732340656... - Vaclav Kotesovec, Sep 11 2021

MAPLE

b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, [1$2],

      (p-> p+[0, p[1]])(b(x-1, y)+b(x, y-1)+b(x-1, y-1)+b(x-1, y+1))))

    end:

a:= n-> b(n, 0)[2]:

seq(a(n), n=0..30);

CROSSREFS

Cf. A225041.

Sequence in context: A309182 A099553 A119694 * A197048 A175613 A296001

Adjacent sequences:  A286757 A286758 A286759 * A286761 A286762 A286763

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 14 2017

STATUS

approved

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Last modified October 24 03:27 EDT 2021. Contains 348217 sequences. (Running on oeis4.)