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A244524
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Number of pairs (f,g) of commuting maps {0,..,n-1}->{0,..,n-1} with 0 <= f(k), g(k) <= k.
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0
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1, 1, 4, 26, 236, 2780, 40642, 715836, 14873174, 358866952, 9934283924, 312461402424
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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 ]
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MAPLE
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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)):
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CROSSREFS
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Cf. A181162 (commuting maps {{1,..,n}->{1,..,n} without restrictions).
Cf. A053529 (commuting permutations).
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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