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Revision History for A112091 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Number of idempotent order-preserving partial transformations (of an n-element chain).
(history; published version)
#44 by Michael De Vlieger at Sat Sep 07 08:53:03 EDT 2024
STATUS

reviewed

approved

#43 by Stefano Spezia at Sat Sep 07 08:42:01 EDT 2024
STATUS

proposed

reviewed

#42 by Michel Marcus at Sat Sep 07 01:11:42 EDT 2024
STATUS

editing

proposed

#41 by Michel Marcus at Sat Sep 07 01:11:35 EDT 2024
LINKS

D. Callan, and T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 [math.CO] (2017), Table 2 No 200 (offset 1 then).

A. Laradji, A. and A. Umar, <a href="http://dx.doi.org/10.1016/j.jalgebra.2003.10.023">A. Combinatorial results for semigroups of order-preserving partial transformations</a>, Journal of Algebra 278, (2004), 342-359.

A. Laradji, A. and A. Umar, A. <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Umar/um.html">Combinatorial results for semigroups of order-decreasing partial transformations</a>, J. Integer Seq. 7 (2004), 04.3.8

STATUS

reviewed

editing

#40 by Andrew Howroyd at Fri Sep 06 23:47:50 EDT 2024
STATUS

proposed

reviewed

#39 by Jason Yuen at Fri Sep 06 23:17:23 EDT 2024
STATUS

editing

proposed

#38 by Jason Yuen at Fri Sep 06 23:16:47 EDT 2024
FORMULA

a(n) = ((sqrt(5))^(n - 1))*(((sqrt(5) + 1)/2)^n - ((sqrt(5) - 1)/2)^n)); a(n) = 1 + 5*(a(n-1) - a(n-2)), a(0) = 1, a(1) = 2. [corrected by _Jason Yuen_, Sep 06 2024]

a(n) = 1 + 5*(a(n-1) - a(n-2)), a(0) = 1, a(1) = 2.

STATUS

approved

editing

Discussion
Fri Sep 06
23:17
Jason Yuen: Added "+ 1" to the formula.
#37 by Charles R Greathouse IV at Thu Sep 08 08:45:21 EDT 2022
PROG

(MAGMAMagma) [ n eq 1 select 1 else n eq 2 select 2 else n eq 3 select 6 else 6*Self(n-1)-10*Self(n-2)+ 5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 21 2011

Discussion
Thu Sep 08
08:45
OEIS Server: https://oeis.org/edit/global/2944
#36 by Peter Luschny at Fri Nov 09 04:16:53 EST 2018
STATUS

reviewed

approved

#35 by Michel Marcus at Fri Nov 09 01:18:07 EST 2018
STATUS

proposed

reviewed