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%I #14 Feb 19 2024 01:49:04
%S 0,0,2,2,6,4,14,12,28,24,62,54,126,112,246,240,510,476,1022,990,2030,
%T 1984,4094,4020,8184,8064,16352,16254,32766,32484,65534,65280,131006,
%U 130560,262122,261576,524286,523264,1048446,1047540,2097150,2094988,4194302,4192254
%N Number of primitive (aperiodic) palindromes using exactly two different symbols.
%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="/A056463/b056463.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{d|n} mu(d)*A056453(n/d).
%F G.f.: Sum_{k>=1} mu(k)*2*x^(3*k)/((1 - 2*x^(2*k))*(1 - x^k)). - _Andrew Howroyd_, Sep 29 2019
%o (PARI) seq(n)={Vec(sum(k=1, n\3, moebius(k)*2*x^(3*k)/((1 - 2*x^(2*k))*(1 - x^k)) + O(x*x^n)), -n)} \\ _Andrew Howroyd_, Sep 29 2019
%o (Python)
%o from sympy import mobius, divisors
%o def A056463(n): return sum(mobius(n//d)*((1<<(d+1>>1))-2) for d in divisors(n, generator=True)) # _Chai Wah Wu_, Feb 18 2024
%Y Column 2 of A327873.
%Y Cf. A056453, A056458.
%K nonn
%O 1,3
%A _Marks R. Nester_
%E Terms a(32) and beyond from _Andrew Howroyd_, Sep 28 2019
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