

A093367


Number of nbead necklaces using exactly three colors with no adjacent beads having the same color.


2



0, 0, 2, 3, 6, 11, 18, 33, 58, 105, 186, 349, 630, 1179, 2190, 4113, 7710, 14599, 27594, 52485, 99878, 190743, 364722, 699249, 1342182, 2581425, 4971066, 9587577, 18512790, 35792565, 69273666, 134219793, 260301174, 505294125, 981706830, 1908881897, 3714566310
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OFFSET

1,3


COMMENTS

Original name: number of periodic cycles of iterative map described by Ma and Wainwright.


REFERENCES

David W. Hobill and Scott MacDonald (zeened(AT)shaw.ca), Preprint, 2004.
P. KH. Ma and Wainright, A dynamical systems approach to the oscillatory singularity in Bianchi cosmologies, Relativity Today, 1994.


LINKS



FORMULA



EXAMPLE

a(3) = 2 because the two necklaces 123 and 132 have no adjacent equal elements.  Andrew Howroyd, Dec 21 2019


MATHEMATICA

Table[Mod[n, 2]  3 + DivisorSum[n, EulerPhi[n/#] 2^# &]/n, {n, 37}] (* Michael De Vlieger, Dec 22 2019 *)


PROG

(PARI) a(n)={n%2  3 + sumdiv(n, d, eulerphi(n/d)*2^d)/n} \\ Andrew Howroyd, Dec 21 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

a(1)a(2) prepended and terms a(20) and beyond from Andrew Howroyd, Dec 21 2019


STATUS

approved



