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Number of primitive (aperiodic) palindromes using a maximum of four different symbols.
4

%I #21 May 04 2023 01:56:27

%S 4,0,12,12,60,48,252,240,1008,960,4092,4020,16380,16128,65460,65280,

%T 262140,261072,1048572,1047540,4194036,4190208,16777212,16772880,

%U 67108800,67092480,268434432,268419060,1073741820,1073675280,4294967292,4294901760,17179865076,17179607040,68719476420

%N Number of primitive (aperiodic) palindromes using a maximum of four 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]

%F a(n) = Sum_{d|n} mu(d)*A056450(n/d).

%o (PARI) a(n) = sumdiv(n, d, moebius(d)*(3*2^(n/d)-(-2)^(n/d))/2);

%o for(n=1, 40, print1(a(n), ", ")); \\ _Petros Hadjicostas_, Apr 24 2020

%Y Column 4 of A284823.

%Y Cf. A056450.

%K nonn

%O 1,1

%A _Marks R. Nester_

%E More terms from _Petros Hadjicostas_, Apr 24 2020