The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A268316 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A268316

a(n) is the number of Dyck paths of length 4n and height n.
(history; published version)

#44 by Charles R Greathouse IV at Thu Sep 08 08:46:15 EDT 2022

PROG

(MAGMAMagma) [Binomial(4*n, n)*2*(2*n+3)*(2*n^2+1)/((3*n+1)*(3*n+2)*(3*n+3)): n in [1..30]]; // Vincenzo Librandi, Feb 04 2016

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#43 by Alois P. Heinz at Thu Jul 06 18:35:41 EDT 2017

STATUS

editing

approved

#42 by Alois P. Heinz at Thu Jul 06 17:01:03 EDT 2017

CROSSREFS

Column k=2 of A289481.

STATUS

approved

editing

#41 by N. J. A. Sloane at Thu Dec 22 22:17:04 EST 2016

STATUS

editing

approved

#40 by N. J. A. Sloane at Thu Dec 22 22:17:00 EST 2016

DATA

1, 1, 7, 57, 484, 4199, 36938, 328185, 2937932, 26457508, 239414383, 2175127695, 19827974412, 181266501290, 1661241473220, 15257624681145, 140400178555644, 1294141164447692, 11946771748196428, 110435320379615620, 1022108852175416720, 9470416604629933935

OFFSET

1,2

0,3

LINKS

Gheorghe Coserea, <a href="/A268316/b268316.txt">Table of n, a(n) for n = 10..1000</a>.

EXTENSIONS

Added a(0)=1, adjusted b-file - N. J. A. Sloane, Dec 22 2016

STATUS

proposed

editing

#39 by Gheorghe Coserea at Thu Dec 22 18:19:25 EST 2016

STATUS

editing

proposed

Discussion

Thu Dec 22

18:47

Alois P. Heinz: This sequence should have a(0)=1.

20:20

Gheorghe Coserea: the main reason for selecting offset 1 was that A080936 is not defined in 0,0 ...

20:21

Gheorghe Coserea: but you right about a(0)=1.

#38 by Gheorghe Coserea at Thu Dec 22 18:18:05 EST 2016

LINKS

Gheorghe Coserea, <a href="/A268316/b268316.txt">Table of n, a(n) for n = 1..1000</a> Gheorghe Coserea, <a href="/A268316/a268316.mzn.txt">MiniZinc model for generating solutions</a>.

Gheorghe Coserea, <a href="/A268316/a268316.mzn.txt">MiniZinc model for generating solutions</a>.

Discussion

Thu Dec 22

18:19

Gheorghe Coserea: I forgot to sort the solutions files, so I re-uploaded them sorted.

#37 by Gheorghe Coserea at Thu Dec 22 18:16:43 EST 2016

LINKS

Gheorghe Coserea, <a href="/A268316/a268316_2.txt">Solutions for n=3.</a>.

#36 by Gheorghe Coserea at Thu Dec 22 18:16:23 EST 2016

LINKS

Gheorghe Coserea, <a href="/A268316/a268316_2.txt">Solutions for n=3.</a>

Gheorghe Coserea, <a href="/A268316/a268316_3.txt">Solutions for n=4</a>.

#35 by Gheorghe Coserea at Thu Dec 22 18:13:33 EST 2016

LINKS

Gheorghe Coserea, <a href="/A268316/b268316.txt">Table of n, a(n) for n = 1..1000</a> Gheorghe Coserea, <a href="/A268316/a268316.mzn.txt">MiniZinc model for generating solutions</a>.

Gheorghe Coserea, <a href="/A268316/a268316.txt">Solutions for n=3</a>.

Gheorghe Coserea, <a href="/A268316/a268316_1.txt">Solutions for n=4</a>.

Gheorghe Coserea, <a href="/A268316/a268316.mzn.txt">MiniZinc model for generating solutions</a>.

STATUS

proposed

editing