A107848 Number of subsets of the n-th roots of unity summing to a real number.

2, 4, 4, 8, 8, 24, 16, 48, 40, 144, 64, 336, 128, 864, 416, 1728, 512, 8304, 1024, 10656, 4032, 31104, 4096, 116256, 9248, 186624, 40000, 374976, 32768, 3537024, 65536, 2239488

Offset: 1

Author

T. D. Noe, May 25 2005

Keywords

• nonn

Links

• T. D. Noe, Sums of Roots of Unity Plots

Crossrefs

Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).

Programs

Mathematica

Needs["DiscreteMath`Combinatorica`"]; Table[Plus@@Table[Count[(KSubsets[Range[n], k]), q_List/;Im[Chop[Plus@@(E^(2.*Pi*I*q/n))]]==0], {k, 0, n}], {n, 20}]

Formula

For prime n, a(n)=2^((n+1)/2).