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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.

%I A108416 #7 Oct 28 2021 06:30:34
%S A108416 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,
%T A108416 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,
%U A108416 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
%N 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.
%C A108416 Row n is divisible by n (rotation symmetry).
%C A108416 Row sums: A108417.
%e A108416 T(6,2)=6, counting {1,3}, {1,5}, {2,4}, {2,6}, {3,5}, {4,6}.
%e A108416 Table starts:
%e A108416   0,
%e A108416   0, 1,
%e A108416   0, 2, 0,
%e A108416   0, 3, 3, 0,
%e A108416   0, 4, 0, 4, 0,
%e A108416   0, 5, 0, 0, 5, 0,
%e A108416   0, 6, 6,12, 6, 6, 0,
%e A108416   0, 7, 0, 0, 0, 0, 7, 0,
%e A108416   0, 8, 0,24, 0,24, 0, 8, 0,
%e A108416   0, 9, 9, 0,18,18, 0, 9, 9, 0
%t A108416 <<DiscreteMath`Combinatorica`; Table[Count[KSubsets[Range[n], k], q_List/;Chop[ -1+Abs[Plus @@ (E^((2.*Pi*I*q)/n))]] === 0], {n, 16}, {k, 0, n}]
%Y A108416 Cf. A107754, A103314, A108417.
%K A108416 nonn,tabl
%O A108416 0,5
%A A108416 _Wouter Meeussen_, Jun 02 2005