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A208595
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Number of n-bead necklaces labeled with numbers -6..6 not allowing reversal, with sum zero.
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2
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1, 7, 43, 371, 3431, 34153, 353333, 3770475, 41165305, 457714497, 5164908167, 58997692301, 680874861687, 7926902673655, 92986983743513, 1097999648804923, 13040634990748733, 155677447454317639, 1866995100779692627, 22482675584863229261
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OFFSET
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1,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201550(d). - Andrew Howroyd, Mar 02 2017
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EXAMPLE
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Some solutions for n=4:
.-4...-5...-4...-6...-5...-3...-4...-1...-4...-6...-6...-4...-6...-1...-5...-4
..4....2...-3....5....0....1....0....0....2...-1....3....2....5...-1....4....2
..0...-1....4....1....0....2...-1....0...-3....1....2...-2...-4....0....2....4
..0....4....3....0....5....0....5....1....5....6....1....4....5....2...-1...-2
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MATHEMATICA
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comps[r_, m_, k_] := Sum[(-1)^i*Binomial[r - 1 - i*m, k - 1]*Binomial[k, i], {i, 0, Floor[(r - k)/m]}]; a[n_Integer, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] = a[n, 6]; Array[a, 20] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)
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CROSSREFS
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Column 6 of A208597.
Sequence in context: A193705 A164775 A127999 * A121675 A243273 A292502
Adjacent sequences: A208592 A208593 A208594 * A208596 A208597 A208598
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Feb 29 2012
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EXTENSIONS
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a(15)-a(20) from Andrew Howroyd, Mar 02 2017
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STATUS
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approved
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