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A208590 Number of n-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero. 2
1, 3, 13, 125, 1761, 34153, 833253, 24627705, 855798877, 34223775091, 1549090700059, 78325577416281, 4376902102440375, 267933660979057571, 17834397187887850661, 1282662234529669344753, 99133711906097886767313, 8194555387462964814207631 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 02:46 EST 2023. Contains 360082 sequences. (Running on oeis4.)