|
%I #15 Nov 01 2017 12:24:12
%S 1,2,3,6,11,26,57,142,351,902,2333,6166,16381,44046,119183,324862,
%T 890291,2453126,6789309,18869426,52635789,147325510,413618615,
%U 1164517198,3287073461,9300516890,26372968983,74937177538,213333642443,608400919106,1737954608281
%N Number of n-bead necklaces labeled with numbers -1..1 not allowing reversal, with sum zero.
%H Andrew Howroyd, <a href="/A208602/b208602.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A002426(d). - _Andrew Howroyd_, Mar 02 2017
%e All solutions for n=5:
%e .-1...-1...-1...-1...-1...-1...-1...-1....0...-1...-1
%e .-1....1....0...-1....0....0....0....0....0....1...-1
%e ..1...-1....0....1....1...-1....1....0....0....0....0
%e ..1....1....1....0...-1....1....0....0....0....0....1
%e ..0....0....0....1....1....1....0....1....0....0....1
%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, 1]; Array[a, 31] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%Y Column 1 of A208597.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 29 2012
|
