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A208593
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Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero.
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2
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1, 5, 21, 125, 791, 5457, 39019, 288317, 2178929, 16773395, 131034839, 1036252649, 8279446917, 66733111919, 541954722471, 4430427981533, 36428763143945, 301074015186469, 2499725665085301, 20840038803521835, 174388665638906551, 1464205768804076875
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history;
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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) * A025014(d). - Andrew Howroyd, Mar 02 2017
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EXAMPLE
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All solutions for n=3:
.-4...-2...-2...-3...-1...-3...-2...-3...-3...-4....0...-3...-2...-4...-1...-4
..2...-1....2....1....1....2....3...-1....3....1....0....0....0....0....0....3
..2....3....0....2....0....1...-1....4....0....3....0....3....2....4....1....1
..
.-1...-4...-3...-2...-2
.-1....4....4....1...-2
..2....0...-1....1....4
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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, 4]; Array[a, 22] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)
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CROSSREFS
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Column 4 of A208597.
Sequence in context: A218962 A124311 A353736 * A213009 A316102 A352388
Adjacent sequences: A208590 A208591 A208592 * A208594 A208595 A208596
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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(16)-a(22) from Andrew Howroyd, Mar 02 2017
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STATUS
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approved
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