A284841 Number of primitive (aperiodic) palindromic structures of length n using an infinite alphabet.

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

Author

Andrew Howroyd, Apr 03 2017

Keywords

• nonn

Comments

Permuting the symbols will not change the structure.

Examples

			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
		

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

Crossrefs

Row sums of A284826.

Cf. A000110, A082951, A034743.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];
Array[a, 34] (* Jean-François Alcover, Jun 06 2017 *)

PARI

bell(n) = sum(k=0,n,stirling(n,k,2));
a(n) = sumdiv(n,d, moebius(n/d) * bell(ceil(d/2)));

Formula

a(n) = Sum_{k=1..ceiling(n/2)} A284826(n,k).

a(n) = Sum_{d | n} mu(n/d) * Bell(ceiling(d/2)).