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%I #11 Jun 29 2018 05:06:06
%S 1,1,2,4,9,16,35,66,133,261,527,1032,2079,4123,8244,16440,32895,65639,
%T 131327,262380,524762,1049071,2098175,4195230,8390646,16779231,
%U 33558392,67112892,134225919,268443306
%N Number of primitive (aperiodic) reversible string structures with n beads using a maximum of two different colors.
%C A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure.
%D M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%F a(n) = sum mu(d)*A005418(n/d) where d divides n.
%t a[n_] := DivisorSum[n, MoebiusMu[#] (2^(n/#-2) + 2^(Floor[n/#/2]-1))&];
%t Array[a, 30] (* _Jean-François Alcover_, Jun 29 2018 *)
%Y Cf. A045625.
%K nonn
%O 1,3
%A _Marks R. Nester_