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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Column 7 of A208597.

Sequence in context: A199555 A241594 A241595 * A324205 A002402 A015464

Adjacent sequences: A208593 A208594 A208595 * A208597 A208598 A208599

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

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

Status

approved