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A208593 Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero. 2
1, 5, 21, 125, 791, 5457, 39019, 288317, 2178929, 16773395, 131034839, 1036252649, 8279446917, 66733111919, 541954722471, 4430427981533, 36428763143945, 301074015186469, 2499725665085301, 20840038803521835, 174388665638906551, 1464205768804076875 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 01 2017, after Andrew Howroyd *)

CROSSREFS

Column 4 of A208597.

Sequence in context: A002711 A218962 A124311 * A213009 A316102 A050910

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

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Last modified September 28 19:16 EDT 2021. Contains 347717 sequences. (Running on oeis4.)