A107754 Number of subsets of the n-th roots of unity that sum to 1.

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

1,4

Links

Table of n, a(n) for n=1..32.

Formula

For prime p, a(p^i) = 2^(p^(i-1)-1).

Mathematica

<< 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 *)

Crossrefs

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).

Sequence in context: A364829 A264859 A007956 * A181569 A274085 A302129

Adjacent sequences: A107751 A107752 A107753 * A107755 A107756 A107757

Keyword

nonn,more

Author

T. D. Noe, May 23 2005

Status

approved