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This is the case k = 3 of the number of orbits of the group of units of Z/(n) acting naturally on the k-subsets of Z/(n).
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%I #9 Apr 23 2023 07:29:49

%S 1,3,3,12,7,20,16,32,17,72,25,64,65,89,43,148,55,172,123,156,81,334,

%T 118,220,175,322,131,556,151,374,291,376,289,735,217,472,405,766,267,

%U 1028,295,760,659,692,353,1368,446,1008,685,1054,451,1484,681,1398,855

%N This is the case k = 3 of the number of orbits of the group of units of Z/(n) acting naturally on the k-subsets of Z/(n).

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

%Y Cf. A063379, A063381, A000005, A056376 + 1, A056371 - 1.

%K nonn

%O 3,2

%A _W. Edwin Clark_, Jul 15 2001

%E More terms from _Sean A. Irvine_, Apr 22 2023