A208596 Number of n-bead necklaces labeled with numbers -7..7 not allowing reversal, with sum zero.

1, 8, 57, 568, 6077, 69784, 833253, 10259448, 129245091, 1658145128, 21589248803, 284548542120, 3789094334455, 50900085245304, 688944374917247, 9386664978851448, 128633790260673263, 1771859642698543096, 24518513933529549357, 340679786167936420216

Offset: 1

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn

Examples

			Some solutions for n=4:
.-4...-7...-7...-7...-4...-3...-3...-5...-2...-5...-7...-6...-6...-7...-6...-7
..0....4...-1....6....2...-3...-1....1....0...-3....6....3....5....1...-1...-2
..6....3....2...-1....1...-1...-2....7....1....3...-3...-3....5....7....0....4
.-2....0....6....2....1....7....6...-3....1....5....4....6...-4...-1....7....5
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Column 7 of A208597.

Programs

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

Formula

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201551(d). - Andrew Howroyd, Mar 02 2017

Extensions

a(14)-a(20) from Andrew Howroyd, Mar 02 2017