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

%I A284841 #19 Oct 02 2017 16:17:05
%S A284841 1,0,1,1,4,3,14,13,50,47,202,197,876,862,4134,4125,21146,21092,115974,
%T A284841 115922,678554,678367,4213596,4213381,27644432,27643560,190899270,
%U A284841 190898444,1382958544,1382954355,10480142146,10480138007,82864869600,82864848657
%N A284841 Number of primitive (aperiodic) palindromic structures of length n using an infinite alphabet.
%C A284841 Permuting the symbols will not change the structure.
%D A284841 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 A284841 Andrew Howroyd, <a href="/A284841/b284841.txt">Table of n, a(n) for n = 1..200</a>
%F A284841 a(n) = Sum_{k=1..ceiling(n/2)} A284826(n,k).
%F A284841 a(n) = Sum_{d | n} mu(n/d) * Bell(ceiling(d/2)).
%e A284841 n = 1: a => 1
%e A284841 n = 3: aba => 1
%e A284841 n = 4: abba => 1
%e A284841 n = 5: aabaa, ababa, abbba, abcba => 4
%e A284841 n = 6: aabbaa, abbbba, abccba => 3
%t A284841 a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];
%t A284841 Array[a, 34] (* _Jean-François Alcover_, Jun 06 2017 *)
%o A284841 (PARI)
%o A284841 bell(n) = sum(k=0,n,stirling(n,k,2));
%o A284841 a(n) = sumdiv(n,d, moebius(n/d) * bell(ceil(d/2)));
%Y A284841 Row sums of A284826.
%Y A284841 Cf. A000110, A082951, A034743.
%K A284841 nonn
%O A284841 1,5
%A A284841 _Andrew Howroyd_, Apr 03 2017