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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 (list; graph; refs; listen; history; text; internal format)
 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] LINKS Table of n, a(n) for n=1..26. 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 Cf. A001998, A056314. Sequence in context: A080097 A096886 A176904 * A091588 A297219 A018046 Adjacent sequences: A056329 A056330 A056331 * A056333 A056334 A056335 KEYWORD nonn AUTHOR Marks R. Nester STATUS approved

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Last modified June 8 11:34 EDT 2023. Contains 363164 sequences. (Running on oeis4.)