A327612 Number of length n reversible string structures that are not palindromic using any number of colors.

0, 1, 2, 9, 27, 112, 453, 2137, 10691, 58435, 340187, 2110016, 13829358, 95474679, 691538954, 5240280999, 41432965441, 341040295916, 2916376121375, 25862097370783, 237434958512487, 2253358056604465, 22076003464423853, 222979436686398848, 2319295172150784296

Offset: 1

Author

Andrew Howroyd, Sep 18 2019

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Row sums of A309748(n > 1).

Cf. A103293, A188164, A304972.

Programs

PARI

\\ Ach is A304972 as square matrix.
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}
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)))}

Formula

a(n) = A103293(n + 1) - A188164(n).