The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A089849

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A089849

Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A069772.
(history; published version)

#38 by Peter Luschny at Mon Jun 17 07:10:34 EDT 2024

STATUS

reviewed

approved

#37 by Joerg Arndt at Mon Jun 17 06:44:33 EDT 2024

STATUS

proposed

reviewed

#36 by Michel Marcus at Mon Jun 17 06:34:59 EDT 2024

STATUS

editing

proposed

Discussion

Mon Jun 17

06:44

Joerg Arndt: it used to be so (and is unless I missed an important meeting)

#35 by Michel Marcus at Mon Jun 17 06:34:39 EDT 2024

FORMULA

a(n+1) = (Sum_{k=0..n} C(n,k)*C(n+2,k)*(-1)^k)*(cos(Pi*n/2)+sin(Pi*n/2)). (End)

Discussion

Mon Jun 17

06:34

Michel Marcus: C(k) is Catalan, C(n,k) is binomial; ok ?

#34 by Michel Marcus at Mon Jun 17 06:34:20 EDT 2024

FORMULA

a(n) = Sum_{k=0..floor(n/2)} C(k)*C(k+1,n-k). - Paul Barry, Feb 23 2005

a(n+1) = (Sum_{k=0..n} C(n,k)*C(n+2,k)(-1)^k)*(cos(Pi*n/2)+sin(Pi*n/2)). (End)

STATUS

approved

editing

#33 by Michel Marcus at Sun Mar 12 04:21:31 EDT 2023

STATUS

reviewed

approved

#32 by Joerg Arndt at Sun Mar 12 04:13:40 EDT 2023

STATUS

proposed

reviewed

#31 by Amiram Eldar at Sun Mar 12 01:35:01 EST 2023

STATUS

editing

proposed

#30 by Amiram Eldar at Sun Mar 12 01:31:47 EST 2023

LINKS

A. Antti Karttunen, <a href="/A089408/a089408.c.txt">C-program for computing the initial terms of this sequence</a>.

#29 by Amiram Eldar at Sun Mar 12 01:31:20 EST 2023

FORMULA

From Amiram Eldar, Mar 12 2023: (Start)

Sum_{n>=0} 1/a(n) = 10/3 + 2*Pi/(3*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 2/3 + 2*Pi/(9*sqrt(3)). (End)

STATUS

approved

editing