The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A224769 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A224769

Number of lattice paths from (0,0) to (n,n) that do not go below the x-axis or above the diagonal x=y and consist of steps U=(1,1), D=(1,-1) and S=(0,1).
(history; published version)

#24 by Michel Marcus at Fri Dec 18 12:02:06 EST 2020

STATUS

reviewed

approved

#23 by Vaclav Kotesovec at Fri Dec 18 12:01:51 EST 2020

STATUS

proposed

reviewed

#22 by Jean-François Alcover at Fri Dec 18 09:27:41 EST 2020

STATUS

editing

proposed

#21 by Jean-François Alcover at Fri Dec 18 09:27:37 EST 2020

MATHEMATICA

b[x_, y_] := b[x, y] = If[y > x, 0, If[x == 0, 1, If[y > 0, b[x, y - 1] + b[x - 1, y - 1], 0] + b[x - 1, y + 1]]];

a[n_] := b[n, n];

a /@ Range[0, 30] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *)

STATUS

approved

editing

#20 by OEIS Server at Sun May 14 08:59:59 EDT 2017

LINKS

Alois P. Heinz, <a href="/A224769/b224769_1.txt">Table of n, a(n) for n = 0..1000</a>

#19 by Alois P. Heinz at Sun May 14 08:59:59 EDT 2017

STATUS

editing

approved

Discussion

Sun May 14

08:59

OEIS Server: Installed new b-file as b224769.txt.  Old b-file is now b224769_1.txt.

#18 by Alois P. Heinz at Sun May 14 08:59:54 EDT 2017

LINKS

Alois P. Heinz, <a href="/A224769/b224769_1.txt">Table of n, a(n) for n = 0..5001000</a>

#17 by Alois P. Heinz at Sun May 14 08:53:29 EDT 2017

CROSSREFS

Cf. A198324 (paths to (n,0)), A225042 (with additional H-steps), A286425.

STATUS

approved

editing

#16 by Vaclav Kotesovec at Sun Sep 07 08:36:17 EDT 2014

STATUS

editing

approved

#15 by Vaclav Kotesovec at Sun Sep 07 08:36:10 EDT 2014

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 3/4*(71 + 8*sqrt(2))^(1/3) + 51/(4*(71 + 8*sqrt(2))^(1/3)) + 13/4 = 9.4435356015932520820011..., c = 0.00814413508604516738631686716788556507884786... . - Vaclav Kotesovec, Sep 07 2014

STATUS

approved

editing