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A284841
Number of primitive (aperiodic) palindromic structures of length n using an infinite alphabet.
4
1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 202, 197, 876, 862, 4134, 4125, 21146, 21092, 115974, 115922, 678554, 678367, 4213596, 4213381, 27644432, 27643560, 190899270, 190898444, 1382958544, 1382954355, 10480142146, 10480138007, 82864869600, 82864848657
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
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
Row sums of A284826.
Sequence in context: A056478 A056479 A056480 * A334752 A197883 A222195
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 03 2017
STATUS
approved