A056281 - OEIS

%I #16 Apr 15 2021 21:40:42

%S 0,0,0,0,1,15,140,1050,6951,42524,246730,1379385,7508501,40074895,

%T 210766919,1096189500,5652751651,28958088579,147589284710,

%U 749206047975,3791262568261,19137821665325,96416888184100

%N Number of primitive (aperiodic) word structures of length n which contain exactly five different symbols.

%C Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same 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_{n > 0, d|n} mu(d)*A000481(n/d).

%F G.f.: Sum_{k>=1} mu(k) * x^(5*k) / Product_{j=1..5} (1 - j*x^k). - _Ilya Gutkovskiy_, Apr 15 2021

%Y Column 5 of A137651.

%Y Cf. A056270.

%K nonn

%O 1,6

%A _Marks R. Nester_