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A056278
Number of primitive (aperiodic) word structures of length n which contain exactly two different symbols.
5
0, 1, 3, 6, 15, 27, 63, 120, 252, 495, 1023, 2010, 4095, 8127, 16365, 32640, 65535, 130788, 262143, 523770, 1048509, 2096127, 4194303, 8386440, 16777200, 33550335, 67108608, 134209530, 268435455, 536854005, 1073741823, 2147450880, 4294966269, 8589869055, 17179869105
OFFSET
1,3
COMMENTS
Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same structure. This is identical to A000740 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
FORMULA
a(n) = Sum_{d|n} mu(d)*A000225(n/d-1) where n>0.
G.f.: Sum_{k>=1} mu(k) * x^(2*k) / ((1 - x^k) * (1 - 2*x^k)). - Ilya Gutkovskiy, Apr 15 2021
CROSSREFS
Apart from initial term, this is a duplicate of A000740.
Column 2 of A137651.
Cf. A056267.
Sequence in context: A165729 A348378 A000740 * A161625 A234848 A300761
KEYWORD
nonn
EXTENSIONS
Terms a(30) and beyond from Andrew Howroyd, Apr 15 2021
STATUS
approved