login
A056304
Number of primitive (period n) n-bead necklace structures using exactly three different colored beads.
5
0, 0, 1, 2, 5, 17, 43, 124, 338, 941, 2591, 7234, 20125, 56407, 158349, 446492, 1262225, 3580330, 10181479, 29031306, 82968799, 237642659, 682014587, 1960974220, 5647919640, 16292741605, 47069104274, 136166647110, 394418199725, 1143821887473, 3320790074371
OFFSET
1,4
COMMENTS
Turning over the necklace is not allowed. Colors may be permuted without changing the necklace structure.
REFERENCES
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]
FORMULA
a(n) = Sum_{d|n} mu(d)*A056296(n/d), where mu = A008683 is the Möbius function.
a(n) = A002075(n) - A000048(n).
CROSSREFS
Column 3 of A107424.
Sequence in context: A300692 A076076 A136194 * A063106 A096295 A215580
KEYWORD
nonn
EXTENSIONS
a(28)-a(31) from Pontus von Brömssen, Aug 04 2024
STATUS
approved