A063381 Number of orbits of the group of units of Z/(n) acting naturally on the 4-subsets of Z/(n).

1, 2, 9, 7, 24, 24, 56, 34, 151, 62, 173, 187, 264, 151, 530, 218, 679, 528, 737, 405, 1558, 638, 1256, 1002, 1871, 852, 3567, 1053, 2472, 2109, 2908, 2226, 5433, 1840, 4113, 3523, 6356, 2537, 9598, 2944, 7311, 6424, 7429, 3883, 13592, 5058, 11576, 7982, 12123, 5638, 17971, 8613, 16766, 11201

Offset

4,2

Links

Table of n, a(n) for n=4..57.

Example

a(5) = 2 since when U(5) = {1,2,3,4} acts naturally on the five 4-subsets {0,1,2,3}, {0,1,2,4}, {0,1,3,4}, {0,2,3,4}, {1,2,3,4} of Z/(5) the orbits are {{0,1,2,3},{0,1,2,4}, {0,1,3,4}, {0,2,3,4}} and {{1,2,3,4}}.

Maple

g:= proc(n) local U, S, C, R, u, s, Cr, us, v;
  U:= select(t -> igcd(n, t)=1, [$1..n-1]);
  S:= combinat:-choose({$0..n-1}, 4);
  C:= S;
  for s in S do R[s]:= s od;
  for u in U do
    Cr:= NULL;
    for s in C do
      us:= map(t -> u*t mod n, s);
      v:= R[us];
      while R[v] <> v do v:= R[v] od;
      if v <> s then R[s]:= v; Cr:= Cr, s fi
    od;
    C:= C minus {Cr};
  od;
  nops(C)
end proc;
map(g, [$4..60]); # Robert Israel, Nov 28 2022

Crossrefs

Cf. A063379, A065957, A000005, A056376 + 1, A056371 - 1

Sequence in context: A245287 A254595 A137453 * A019078 A205384 A340724

Adjacent sequences: A063378 A063379 A063380 * A063382 A063383 A063384

Keyword

nonn

Author

W. Edwin Clark, Jul 15 2001

Extensions

Offset corrected, and more terms by Robert Israel, Nov 28 2022

Status

approved