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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

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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: A203320 A005980 A128093 * A056331 A203318 A393352