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)

#34 by Gheorghe Coserea at Thu Dec 22 18:07:13 EST 2016

STATUS

editing

proposed

#33 by Gheorghe Coserea at Thu Dec 22 18:07:09 EST 2016

LINKS

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

#32 by Gheorghe Coserea at Thu Dec 22 18:06:13 EST 2016

LINKS

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

#31 by Gheorghe Coserea at Thu Dec 22 18:05:30 EST 2016

LINKS

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

STATUS

approved

editing

#30 by Vaclav Kotesovec at Sat Aug 13 11:05:09 EDT 2016

STATUS

proposed

approved

#29 by Vaclav Kotesovec at Wed Aug 10 03:36:06 EDT 2016

STATUS

editing

proposed

#28 by Vaclav Kotesovec at Wed Aug 10 03:34:28 EDT 2016

FORMULA

Recurrence: 3*(n+1)*(2*n + 1)*(3*n + 1)*(3*n + 2)*(2*n^2 - 4*n + 3)*a(n) = 8*(2*n - 1)*(2*n + 3)*(4*n - 3)*(4*n - 1)*(2*n^2 + 1)*a(n-1). - Vaclav Kotesovec, Aug 10 2016

#27 by Vaclav Kotesovec at Wed Aug 10 03:30:48 EDT 2016

FORMULA

G.f.: -((3F2(-3/4, -1/2, -1/4; 1/3, 2/3; 256*x/27)-1)/(4*x)) + 4/5*x*3F2(5/4, 3/2, 7/4; 7/3, 8/3; 256*x/27) + 8/3*x^2*3F2(9/4, 5/2, 11/4; 10/3, 11/3; 256*x/27). - _Benedict W. J. Irwin_, Aug 09 2016

-((3F2(-3/4, -1/2, -1/4; 1/3, 2/3; 256*x/27)-1)/(4*x)) + 4/5*x*3F2(5/4, 3/2, 7/4; 7/3, 8/3; 256*x/27) + 8/3*x^2*3F2(9/4, 5/2, 11/4; 10/3, 11/3; 256*x/27). - Benedict W. J. Irwin, Aug 09 2016

STATUS

proposed

editing

#26 by Benedict W. J. Irwin at Tue Aug 09 15:25:43 EDT 2016

STATUS

editing

proposed

#25 by Benedict W. J. Irwin at Tue Aug 09 15:01:21 EDT 2016

FORMULA

-((3F2(-3/4, -1/2, -1/4; 1/3, 2/3; 256*x/27)-1)/(4*x)) + 4/5*x*3F2(5/4, 3/2, 7/4; 7/3, 8/3; 256*x/27) + 8/3*x^2 *3F2(9/4, 5/2, 11/4; 10/3, 11/3; 256*x/27). - Benedict W. J. Irwin, Aug 09 2016