login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244524 Number of pairs (f,g) of commuting maps {0,..,n-1}->{0,..,n-1} with 0 <= f(k), g(k) <= k. 0
1, 1, 4, 26, 236, 2780, 40642, 715836, 14873174, 358866952, 9934283924, 312461402424 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..11.

EXAMPLE

The a(3) = 26 pairs of such maps are (dots for zeros in the maps):

01:  [ . . . ]  [ . . . ]

02:  [ . . . ]  [ . . 1 ]

03:  [ . . . ]  [ . . 2 ]

04:  [ . . . ]  [ . 1 . ]

05:  [ . . . ]  [ . 1 1 ]

06:  [ . . . ]  [ . 1 2 ]

07:  [ . . 1 ]  [ . . . ]

08:  [ . . 1 ]  [ . . 1 ]

09:  [ . . 1 ]  [ . 1 2 ]

10:  [ . . 2 ]  [ . . . ]

11:  [ . . 2 ]  [ . . 2 ]

12:  [ . . 2 ]  [ . 1 . ]

13:  [ . . 2 ]  [ . 1 2 ]

14:  [ . 1 . ]  [ . . . ]

15:  [ . 1 . ]  [ . . 2 ]

16:  [ . 1 . ]  [ . 1 . ]

17:  [ . 1 . ]  [ . 1 2 ]

18:  [ . 1 1 ]  [ . . . ]

19:  [ . 1 1 ]  [ . 1 1 ]

20:  [ . 1 1 ]  [ . 1 2 ]

21:  [ . 1 2 ]  [ . . . ]

22:  [ . 1 2 ]  [ . . 1 ]

23:  [ . 1 2 ]  [ . . 2 ]

24:  [ . 1 2 ]  [ . 1 . ]

25:  [ . 1 2 ]  [ . 1 1 ]

26:  [ . 1 2 ]  [ . 1 2 ]

MAPLE

s:= proc(n) option remember; `if`(n=0, [[]],

       map(x-> seq([x[], i], i=1..n), s(n-1)))

    end:

a:= n-> (l-> add(add(`if`([seq(evalb(f[g[i]]=g[f[i]])

    , i=1..n)]=[true$n], 1, 0), g=l), f=l))(s(n)):

seq(a(n), n=0..6);  # Alois P. Heinz, Jul 30 2014

CROSSREFS

Cf. A181162 (commuting maps {{1,..,n}->{1,..,n} without restrictions).

Cf. A053529 (commuting permutations).

Sequence in context: A244451 A001863 A300698 * A209923 A317339 A304338

Adjacent sequences:  A244521 A244522 A244523 * A244525 A244526 A244527

KEYWORD

nonn,more

AUTHOR

Joerg Arndt, Jul 25 2014

EXTENSIONS

All terms corrected (error pointed out by Alois P. Heinz), Joerg Arndt, Jul 30 2014

a(10)-a(11) from Alois P. Heinz, Jul 30 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 10:08 EST 2019. Contains 329261 sequences. (Running on oeis4.)