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A056332
Number of primitive (aperiodic) reversible string structures with n beads using a maximum of three different colors.
3
1, 1, 3, 8, 24, 65, 195, 564, 1677, 4976, 14883, 44452, 133224, 399113, 1196808, 3588840, 10764960, 32289855, 96864963, 290580040, 871725426, 2615132465, 7845353475, 23535926760, 70607649816, 211822550576
OFFSET
1,3
COMMENTS
A string and its reverse are considered to be equivalent. Permuting the colors will not change the 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 mu(d)*A001998(n/d-1) where d|n.
MATHEMATICA
a1998[n_] := If[OddQ[n], (1/4)*(3^n + 4*3^((n-1)/2) + 1), (1/4)*(3^n + 2*3^(n/2) + 1)];
a[n_] := DivisorSum[n, MoebiusMu[#] a1998[n/#-1]&];
Array[a, 26] (* Jean-François Alcover, Jun 29 2018 *)
CROSSREFS
Sequence in context: A080097 A096886 A176904 * A091588 A297219 A018046
KEYWORD
nonn
STATUS
approved