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%I #8 Oct 03 2019 20:40:10
%S 0,1,2,9,27,112,453,2137,10691,58435,340187,2110016,13829358,95474679,
%T 691538954,5240280999,41432965441,341040295916,2916376121375,
%U 25862097370783,237434958512487,2253358056604465,22076003464423853,222979436686398848,2319295172150784296
%N Number of length n reversible string structures that are not palindromic using any number of colors.
%H Andrew Howroyd, <a href="/A327612/b327612.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = A103293(n + 1) - A188164(n).
%o (PARI) \\ Ach is A304972 as square matrix.
%o Ach(n)={my(M=matrix(n, n, i, k, i>=k)); for(i=3, n, for(k=2, n, M[i, k]=k*M[i-2, k] + M[i-2, k-1] + if(k>2, M[i-2, k-2]))); M}
%o seq(n)={my(A=Ach(n)); vector(n, i, sum(k=1, n, (A[i,k] + stirling(i, k, 2))/2 - stirling((i+1)\2, k, 2)))}
%Y Row sums of A309748(n > 1).
%Y Cf. A103293, A188164, A304972.
%K nonn
%O 1,3
%A _Andrew Howroyd_, Sep 18 2019
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