A208594 Number of n-bead necklaces labeled with numbers -5..5 not allowing reversal, with sum zero.

1, 6, 31, 226, 1761, 14838, 129823, 1172298, 10829443, 101888166, 972840341, 9402986626, 91822503449, 904557886854, 8978540544171, 89709076112442, 901536608361003, 9106692124614666, 92411996211470633, 941636535001651066, 9630568821834643189, 98829095219423607906

Offset: 1

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 5 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, 5]; Array[a, 22] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Formula

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201549(d).

Extensions

a(15)-a(22) from Andrew Howroyd, Mar 02 2017