A056331 Number of primitive (aperiodic) reversible string structures with n beads using a maximum of two different colors.

1, 1, 2, 4, 9, 16, 35, 66, 133, 261, 527, 1032, 2079, 4123, 8244, 16440, 32895, 65639, 131327, 262380, 524762, 1049071, 2098175, 4195230, 8390646, 16779231, 33558392, 67112892, 134225919, 268443306, 536887295, 1073758080, 2147515886, 4294999935, 8590000083

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..35.

Formula

a(n) = Sum_{d|n} mu(d)*A005418(n/d).

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] (2^(n/#-2) + 2^(Floor[n/#/2]-1))&];
Array[a, 30] (* Jean-François Alcover, Jun 29 2018 *)

Crossrefs

Cf. A005418, A045625.

Sequence in context: A005980 A128093 A056336 * A203318 A393352 A282776

Adjacent sequences: A056328 A056329 A056330 * A056332 A056333 A056334

Keyword

nonn

Author

Marks R. Nester

Status

approved