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Search: id:A107847
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| A107847 |
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Related to sums of the n-th roots of unity: sums in a circular wedge (excluding the origin). |
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4
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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.
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LINKS
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Max Alekseyev and M. F. Hasler, Table of n, a(n) for n = 1..164
T. D. Noe, Sums of Roots of Unity Plots
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FORMULA
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a(n)=(2^n-A103314(n))/n.
a(n) = A001037(n) - A110981(n). - Max Alekseyev, Jan 14 2008
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CROSSREFS
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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: A165647 A066313 A018499 this_sequence A059966 A095718 A038751
Adjacent sequences: A107844 A107845 A107846 this_sequence A107848 A107849 A107850
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 25 2005
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