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A208596 Number of n-bead necklaces labeled with numbers -7..7 not allowing reversal, with sum zero. 2

%I

%S 1,8,57,568,6077,69784,833253,10259448,129245091,1658145128,

%T 21589248803,284548542120,3789094334455,50900085245304,

%U 688944374917247,9386664978851448,128633790260673263,1771859642698543096,24518513933529549357,340679786167936420216

%N Number of n-bead necklaces labeled with numbers -7..7 not allowing reversal, with sum zero.

%H Andrew Howroyd, <a href="/A208596/b208596.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201551(d). - _Andrew Howroyd_, Mar 02 2017

%e Some solutions for n=4:

%e .-4...-7...-7...-7...-4...-3...-3...-5...-2...-5...-7...-6...-6...-7...-6...-7

%e ..0....4...-1....6....2...-3...-1....1....0...-3....6....3....5....1...-1...-2

%e ..6....3....2...-1....1...-1...-2....7....1....3...-3...-3....5....7....0....4

%e .-2....0....6....2....1....7....6...-3....1....5....4....6...-4...-1....7....5

%t 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, 7]; Array[a, 20] (* _Jean-Fran├žois Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)

%Y Column 7 of A208597.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 29 2012

%E a(14)-a(20) from _Andrew Howroyd_, Mar 02 2017

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Last modified March 22 20:34 EDT 2023. Contains 361433 sequences. (Running on oeis4.)