A107754
Number of subsets of the n-th roots of unity that sum to 1.
Original entry on oeis.org
1, 1, 1, 2, 1, 6, 1, 8, 4, 18, 1, 60, 1, 66, 20, 128, 1, 600, 1, 612, 68, 1026, 1, 6000, 16, 4098, 256, 8580, 1, 95226, 1, 32768
Offset: 1
Cf.
A103314 (number of subsets of the n-th roots of unity summing to zero) and
A108417 (number of subsets of the n-th roots of unity summing to the absolute value of 1).
-
<< DiscreteMath`Combinatorica`; f[n_] := Plus @@ Table[ Count[ KSubsets[ Range[n], k], q_List /; Chop[ -1 + Plus @@ (E^((2.*Pi*I*q)/n))] === 0], {k, 0, n}]; Table[ f[n], {n, 24}] (* Robert G. Wilson v, Jun 03 2005 *)
A108416
Triangle read by rows: T(n,k) counts the k-subsets of the n-th roots of 1 with absolute value of sum=1.
Original entry on oeis.org
0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 0, 5, 0, 0, 6, 6, 12, 0, 7, 0, 0, 0, 8, 0, 24, 0, 0, 9, 9, 0, 18, 0, 10, 0, 40, 10, 60, 0, 11, 0, 0, 0, 0, 0, 12, 12, 60, 72, 144, 120, 0, 13, 0, 0, 0, 0, 0, 0, 14, 0, 84, 0, 210, 14, 280, 0, 15, 15, 0, 75, 60, 30, 105, 0, 16, 0, 112, 0, 336, 0, 560, 0, 0, 17, 0, 0
Offset: 0
T(6,2)=6, counting {1,3}, {1,5}, {2,4}, {2,6}, {3,5}, {4,6}.
Table starts:
0,
0, 1,
0, 2, 0,
0, 3, 3, 0,
0, 4, 0, 4, 0,
0, 5, 0, 0, 5, 0,
0, 6, 6,12, 6, 6, 0,
0, 7, 0, 0, 0, 0, 7, 0,
0, 8, 0,24, 0,24, 0, 8, 0,
0, 9, 9, 0,18,18, 0, 9, 9, 0
Showing 1-2 of 2 results.
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