A056332 Number of primitive (aperiodic) reversible string structures with n beads using a maximum of three different colors.

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]

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