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 A208602 Number of n-bead necklaces labeled with numbers -1..1 not allowing reversal, with sum zero. 2
 1, 2, 3, 6, 11, 26, 57, 142, 351, 902, 2333, 6166, 16381, 44046, 119183, 324862, 890291, 2453126, 6789309, 18869426, 52635789, 147325510, 413618615, 1164517198, 3287073461, 9300516890, 26372968983, 74937177538, 213333642443, 608400919106, 1737954608281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 FORMULA a(n) = (1/n) * Sum_{d | n} totient(n/d) * A002426(d). - Andrew Howroyd, Mar 02 2017 EXAMPLE All solutions for n=5: .-1...-1...-1...-1...-1...-1...-1...-1....0...-1...-1 .-1....1....0...-1....0....0....0....0....0....1...-1 ..1...-1....0....1....1...-1....1....0....0....0....0 ..1....1....1....0...-1....1....0....0....0....0....1 ..0....0....0....1....1....1....0....1....0....0....1 MATHEMATICA 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, 1]; Array[a, 31] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *) CROSSREFS Column 1 of A208597. Sequence in context: A107113 A156807 A032256 * A051603 A094927 A024423 Adjacent sequences:  A208599 A208600 A208601 * A208603 A208604 A208605 KEYWORD nonn AUTHOR R. H. Hardin, Feb 29 2012 STATUS approved

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Last modified March 21 20:31 EDT 2018. Contains 301041 sequences. (Running on oeis4.)