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A056336 Number of primitive (aperiodic) reversible string structures with n beads using exactly two different colors. 1
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 (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. 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-Fran├žois 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

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)