A208593 Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero.

1, 5, 21, 125, 791, 5457, 39019, 288317, 2178929, 16773395, 131034839, 1036252649, 8279446917, 66733111919, 541954722471, 4430427981533, 36428763143945, 301074015186469, 2499725665085301, 20840038803521835, 174388665638906551, 1464205768804076875

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) * A025014(d). - Andrew Howroyd, Mar 02 2017

Example

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

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

Crossrefs

Column 4 of A208597.

Sequence in context: A218962 A124311 A353736 * A213009 A316102 A352388

Adjacent sequences: A208590 A208591 A208592 * A208594 A208595 A208596

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

a(16)-a(22) from Andrew Howroyd, Mar 02 2017

Status

approved