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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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.

Cf. A000110, A082951, A034743.

Sequence in context: A056478 A056479 A056480 * A197883 A222195 A292413

Adjacent sequences:  A284838 A284839 A284840 * A284842 A284843 A284844

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Apr 03 2017

STATUS

approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)