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Search: a056318 -id:a056318
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Number of primitive (aperiodic) reversible string structures with n beads using exactly two different colors.
+10
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
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]
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.
KEYWORD
nonn
STATUS
approved

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