A056336 Number of primitive (aperiodic) reversible string structures with n beads using exactly two different colors.

0, 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

Offset

1,3

Comments

A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure. Identical to A056331 for n>1.

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..30.

Formula

a(n) = A056331(n) - A063524(n).

Mathematica

a[1] = 0;
a[n_] := DivisorSum[n, MoebiusMu[#] (2^(n/#-2) + 2^(Floor[n/#/2]-1))&];
Array[a, 30] (* Jean-François Alcover, Jun 29 2018 *)

Crossrefs

Column 2 of A276544.

Cf. A056318, A056331, A063524.

Sequence in context: A005980 A128093 A056331 * A203318 A282776 A283015

Adjacent sequences: A056333 A056334 A056335 * A056337 A056338 A056339

Keyword

nonn

Author

Marks R. Nester

Status

approved