A208595 Number of n-bead necklaces labeled with numbers -6..6 not allowing reversal, with sum zero.

1, 7, 43, 371, 3431, 34153, 353333, 3770475, 41165305, 457714497, 5164908167, 58997692301, 680874861687, 7926902673655, 92986983743513, 1097999648804923, 13040634990748733, 155677447454317639, 1866995100779692627, 22482675584863229261

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) * A201550(d). - Andrew Howroyd, Mar 02 2017

Example

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

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, 6]; Array[a, 20] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Crossrefs

Column 6 of A208597.

Sequence in context: A193705 A164775 A127999 * A121675 A243273 A292502

Adjacent sequences: A208592 A208593 A208594 * A208596 A208597 A208598

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

a(15)-a(20) from Andrew Howroyd, Mar 02 2017

Status

approved