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A056331
Number of primitive (aperiodic) reversible string structures with n beads using a maximum of two different colors.
3
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
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]
FORMULA
a(n) = sum mu(d)*A005418(n/d) where d divides n.
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. A045625.
Sequence in context: A203320 A005980 A128093 * A056336 A203318 A282776
KEYWORD
nonn
STATUS
approved