A208590 Number of n-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.

1, 3, 13, 125, 1761, 34153, 833253, 24627705, 855798877, 34223775091, 1549090700059, 78325577416281, 4376902102440375, 267933660979057571, 17834397187887850661, 1282662234529669344753, 99133711906097886767313, 8194555387462964814207631

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..80

Example

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

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_, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] := a[n, n]; Array[a, 18] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Crossrefs

Diagonal of A208597.

Sequence in context: A241458 A302861 A182864 * A228648 A161677 A180276

Adjacent sequences: A208587 A208588 A208589 * A208591 A208592 A208593

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

a(12)-a(18) from Andrew Howroyd, Mar 02 2017

Status

approved