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.

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

0,5

Comments

Row n is divisible by n (rotation symmetry).

Row sums: A108417.

Links

Table of n, a(n) for n=0..85.

Example

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

Mathematica

<<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}]

Crossrefs

Cf. A107754, A103314, A108417.

Sequence in context: A049084 A234580 A352740 * A215395 A338569 A343757

Adjacent sequences: A108413 A108414 A108415 * A108417 A108418 A108419

Keyword

nonn,tabl

Author

Wouter Meeussen, Jun 02 2005

Status

approved