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%I #27 Oct 22 2016 02:05:27
%S 0,0,0,0,0,0,0,1,4,12,30,66,132,245,429,715,1144,1768,2652,3876,5537,
%T 7752,10659,14421,19228,25300,32890,42287,53820,67860,84825,105183,
%U 129456,158224,192129,231880,278256
%N a(n) = floor(C(n,6)/7).
%C a(n-1) is the number of aperiodic necklaces (Lyndon words) with 7 black beads and n-7 white beads.
%H D. J. Broadhurst, <a href="http://arXiv.org/abs/hep-th/9604128">On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory</a>, arXiv:hep-th/9604128, 1996.
%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%F G.f.: (1+x^3)^2/((1-x)^4(1-x^2)^2(1-x^7))*x^7.
%F a(n) = floor(binomial(n+1,7)/(n+1)). [_Gary Detlefs_, Nov 23 2011]
%F G.f.: (x^6/7)*(1/(1-x)^7-1/(1- x^7)). - _Herbert Kociemba_, Oct 16 2016
%t CoefficientList[Series[x^6/7 (1/(1-x)^7-1/(1- x^7)),{x,0,40}],x]; (* _Herbert Kociemba_, Oct 16 2016 *)
%o (PARI) a(n) = binomial(n, 6)\7; \\ _Michel Marcus_, Oct 16 2016
%Y Cf. A000031, A001037, A051168. Same as A051172(n+1).
%Y First differences of A011853.
%Y A column of triangle A011847.
%K nonn,easy
%O 0,9
%A _N. J. A. Sloane_, _David Broadhurst_
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