A107848 - OEIS

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

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OFFSET

1,1

LINKS

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

Yongao Hu, Felix Gerken, and Thore Posske, Hidden Twisted Sectors and Exponential Degeneracy in Root-of-Unity XXZ Heisenberg Chains, arXiv:2602.15098 [cond-mat.stat-mech], 2026. See references.

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

FORMULA

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

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}]

CROSSREFS

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

Sequence in context: A116596 A248692 A048656 * A285273 A353946 A188824

Adjacent sequences: A107845 A107846 A107847 * A107849 A107850 A107851

KEYWORD

nonn

AUTHOR

T. D. Noe, May 25 2005

STATUS

approved