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A208593 Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero. 2

%I #12 Nov 01 2017 12:25:13

%S 1,5,21,125,791,5457,39019,288317,2178929,16773395,131034839,

%T 1036252649,8279446917,66733111919,541954722471,4430427981533,

%U 36428763143945,301074015186469,2499725665085301,20840038803521835,174388665638906551,1464205768804076875

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

%H Andrew Howroyd, <a href="/A208593/b208593.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A025014(d). - _Andrew Howroyd_, Mar 02 2017

%e All solutions for n=3:

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

%e ..2...-1....2....1....1....2....3...-1....3....1....0....0....0....0....0....3

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

%e ..

%e .-1...-4...-3...-2...-2

%e .-1....4....4....1...-2

%e ..2....0...-1....1....4

%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, 4]; Array[a, 22] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)

%Y Column 4 of A208597.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 29 2012

%E a(16)-a(22) from _Andrew Howroyd_, Mar 02 2017

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)