A284841 - OEIS

%I #19 Oct 02 2017 16:17:05

%S 1,0,1,1,4,3,14,13,50,47,202,197,876,862,4134,4125,21146,21092,115974,

%T 115922,678554,678367,4213596,4213381,27644432,27643560,190899270,

%U 190898444,1382958544,1382954355,10480142146,10480138007,82864869600,82864848657

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

%C Permuting the symbols will not change the structure.

%D 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]

%H Andrew Howroyd, <a href="/A284841/b284841.txt">Table of n, a(n) for n = 1..200</a>

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

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

%e n = 1: a => 1

%e n = 3: aba => 1

%e n = 4: abba => 1

%e n = 5: aabaa, ababa, abbba, abcba => 4

%e n = 6: aabbaa, abbbba, abccba => 3

%t a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];

%t Array[a, 34] (* _Jean-François Alcover_, Jun 06 2017 *)

%o (PARI)

%o bell(n) = sum(k=0,n,stirling(n,k,2));

%o a(n) = sumdiv(n,d, moebius(n/d) * bell(ceil(d/2)));

%Y Row sums of A284826.

%Y Cf. A000110, A082951, A034743.

%K nonn

%O 1,5

%A _Andrew Howroyd_, Apr 03 2017