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A056281
Number of primitive (aperiodic) word structures of length n which contain exactly five different symbols.
1
0, 0, 0, 0, 1, 15, 140, 1050, 6951, 42524, 246730, 1379385, 7508501, 40074895, 210766919, 1096189500, 5652751651, 28958088579, 147589284710, 749206047975, 3791262568261, 19137821665325, 96416888184100
OFFSET
1,6
COMMENTS
Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same 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_{n > 0, d|n} mu(d)*A000481(n/d).
G.f.: Sum_{k>=1} mu(k) * x^(5*k) / Product_{j=1..5} (1 - j*x^k). - Ilya Gutkovskiy, Apr 15 2021
CROSSREFS
Column 5 of A137651.
Cf. A056270.
Sequence in context: A354394 A346977 A354398 * A000481 A365528 A327506
KEYWORD
nonn
STATUS
approved