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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Column 5 of A208597.

Sequence in context: A200775 A244255 A299550 * A318539 A221514 A144576

Adjacent sequences: A208591 A208592 A208593 * A208595 A208596 A208597

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

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

Status

approved