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A107847 Related to sums of the n-th roots of unity: sums in a circular wedge (excluding the origin). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

FORMULA

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

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

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.

Sequence in context: A224958 A304912 A018499 * A059966 A095718 A038751

Adjacent sequences:  A107844 A107845 A107846 * A107848 A107849 A107850

KEYWORD

nonn

AUTHOR

T. D. Noe, May 25 2005

STATUS

approved

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Last modified April 20 18:45 EDT 2021. Contains 343137 sequences. (Running on oeis4.)