OFFSET
1,5
COMMENTS
Permuting the symbols 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]
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = Sum_{k=1..ceiling(n/2)} A284826(n,k).
a(n) = Sum_{d | n} mu(n/d) * Bell(ceiling(d/2)).
EXAMPLE
n = 1: a => 1
n = 3: aba => 1
n = 4: abba => 1
n = 5: aabaa, ababa, abbba, abcba => 4
n = 6: aabbaa, abbbba, abccba => 3
MATHEMATICA
a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];
Array[a, 34] (* Jean-François Alcover, Jun 06 2017 *)
PROG
(PARI)
bell(n) = sum(k=0, n, stirling(n, k, 2));
a(n) = sumdiv(n, d, moebius(n/d) * bell(ceil(d/2)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 03 2017
STATUS
approved