A107847 Related to sums of the n-th roots of unity: sums in a circular wedge (excluding the origin).

1, 1, 2, 3, 6, 9, 18, 30, 56, 99, 186, 333, 630, 1161, 2182, 4080, 7710, 14508, 27594, 52371, 99858, 190557, 364722, 698634, 1342176, 2580795, 4971008, 9586377, 18512790, 35786499, 69273666, 134215680, 260300986, 505286415, 981706806

Offset: 1

Author

T. D. Noe, May 25 2005

Keywords

• nonn

Comments

Consider the 2^n sums formed from all the subsets of the n-th roots of unity. The number A103314(n) tells how many of these sums are zero. The remaining sums fall into n wedges centered at the origin. The number a(n) gives the number of sums that fall into each wedge. Interestingly, a(n) coincides with A059966(n) when n is either p^k or pq for primes p and q.

Links

• Max Alekseyev and M. F. Hasler, Table of n, a(n) for n = 1..164
• 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), A107848 (number of subsets of the n-th roots of unity summing to a real number).

Cf. also A110981.

Formula

a(n) = (2^n - A103314(n))/n.

a(n) = A001037(n) - A110981(n). - Max Alekseyev, Jan 14 2008