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A063381
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Number of orbits of the group of units of Z/(n) acting naturally on the 4-subsets of Z/(n).
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2
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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
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OFFSET
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4,2
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LINKS
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EXAMPLE
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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}}.
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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