A056304 - OEIS

%I #16 Aug 04 2024 10:14:10

%S 0,0,1,2,5,17,43,124,338,941,2591,7234,20125,56407,158349,446492,

%T 1262225,3580330,10181479,29031306,82968799,237642659,682014587,

%U 1960974220,5647919640,16292741605,47069104274,136166647110,394418199725,1143821887473,3320790074371

%N Number of primitive (period n) n-bead necklace structures using exactly three different colored beads.

%C Turning over the necklace is not allowed. Colors may be permuted without changing the necklace 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_{d|n} mu(d)*A056296(n/d), where mu = A008683 is the Möbius function.

%F a(n) = A002075(n) - A000048(n).

%Y Column 3 of A107424.

%Y Cf. A000048, A002075, A008683, A056288, A056296.

%K nonn

%O 1,4

%A _Marks R. Nester_

%E a(28)-a(31) from _Pontus von Brömssen_, Aug 04 2024