%I #10 Sep 29 2019 12:02:43
%S 0,1,2,3,6,7,14,18,28,39,62,81,126,175,246,360,510,728,1022,1485,2030,
%T 3007,4094,6030,8184,12159,16352,24381,32766,48849,65534,97920,131006,
%U 196095,262122,392364,524286,785407,1048446,1571310,2097150,3143497,4194302,6288381
%N Number of primitive (period n) periodic palindromes using exactly two different symbols.
%C For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.
%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]
%H Andrew Howroyd, <a href="/A056498/b056498.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{d|n} mu(d)*A027383(n/d-2) assuming that A027383(-1)=0.
%F G.f.: Sum_{k>=1} mu(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))). - _Andrew Howroyd_, Sep 29 2019
%o (PARI) seq(n)={Vec(sum(k=1, n\2, moebius(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))) + O(x*x^n)), -n)} \\ _Andrew Howroyd_, Sep 29 2019
%Y Column 2 of A327878.
%Y Cf. A027383, A056463.
%K nonn
%O 1,3
%A _Marks R. Nester_
%E Terms a(32) and beyond from _Andrew Howroyd_, Sep 28 2019