The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A032349

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A032349

Number of paths from (0,0) to (3n,0) that stay in first quadrant (but may touch horizontal axis), where each step is (2,1),(1,2) or (1,-1) and start with (2,1).
(history; published version)

#44 by N. J. A. Sloane at Wed Nov 22 22:21:17 EST 2023

STATUS

proposed

approved

#43 by Alexander Burstein at Wed Nov 22 21:48:14 EST 2023

STATUS

editing

proposed

#42 by Alexander Burstein at Wed Nov 22 21:47:20 EST 2023

COMMENTS

a(n) is the maximum number of distinct sets that can be obtained as complete parenthesizations of “S_1 union S_2 intersect S_3 union S_4 intersect S_5 union ... union S_{2*n}”, where n union and n-1 intersection operations alternate, starting with a union, and S_1, S_2, ... , S_{2*n} are sets. - Alexander Burstein, Nov 22 2023

STATUS

approved

editing

#41 by Joerg Arndt at Sun May 07 07:21:32 EDT 2023

STATUS

reviewed

approved

#40 by Vaclav Kotesovec at Sun May 07 07:21:24 EDT 2023

STATUS

proposed

reviewed

#39 by Peter Bala at Sun May 07 06:36:28 EDT 2023

STATUS

editing

proposed

#38 by Peter Bala at Sun May 07 06:33:10 EDT 2023

FORMULA

From Peter Bala, May 07 2023: (Start)

n*(2*n-1)*(5*n-9)*a(n) = 2*(55*n^3-209*n^2+255*n-99)*a(n-1) + (n-3)*(2*n-3)*(5*n-4)*a(n-2) with a(1) = 1 and a(2) = 4.

G.f.: A(x) = series reversion of x*(1 - x)^2/(1 + x)^2. - _Peter Bala_, Apr 26 2023(End)

#37 by Peter Bala at Wed Apr 26 08:24:54 EDT 2023

FORMULA

A(x) = series reversion of x*(1 - x)^2/(1 + x)^2. - Peter Bala, Apr 26 2023

KEYWORD

nonn,easy

STATUS

approved

editing

Discussion

Wed May 03

14:14

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A032349 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#36 by Michael De Vlieger at Sat Jul 09 11:07:53 EDT 2022

STATUS

proposed

approved

#35 by Michel Marcus at Sat Jul 09 02:31:09 EDT 2022

STATUS

editing

proposed