A345734 - OEIS

%I #15 Jan 24 2023 23:12:42

%S 1,1,0,1,0,1,0,2,1,4,2,9,6,21,18,48,50,114,135,277,358,681,935,1693,

%T 2425,4235,6258,10643,16085,26852,41226,67921,105456,172125,269375,

%U 436785,687409,1109411,1752966,2819711,4468025,7170045,11384240,18238260,28999047

%N Number of planar vertically indecomposable distributive lattices with n nodes.

%H Andrew Howroyd, <a href="/A345734/b345734.txt">Table of n, a(n) for n = 1..1000</a>

%H Peter Jipsen, <a href="https://math.chapman.edu/~jipsen/tikzsvg/planar-vi-distributive-lattices.html">Planar vertically indecomposable distributive lattices up to size 22</a>, March 2014.

%o (PARI) \\ S is symmetric only, V counts reflections separately.

%o S(n)={my(M=matrix(n, sqrtint(n)), v=vector(n)); for(n=1, n, my(s=0); for(k=2, sqrtint(n), s += (k^2==n) + sum(j=2, k-1, v[n-k^2+j^2] - M[n-k^2+j^2, j]); M[n,k]=s); v[n]=s); v}

%o V(n)={my(M=matrix(n, n\2), v=vector(n)); for(n=1, n, my(s=0); for(k=2, n\2, s += (2*k==n) + sum(j=2, min(k, n-2*k), v[n+j-2*k] - M[n+j-2*k, j-1]); M[n,k]=s); v[n]=s); v}

%o seq(n)={(S(n)+V(n))/2 + vector(n, i, i<=2)} \\ _Andrew Howroyd_, Jan 24 2023

%Y Cf. A072361, A343161.

%K nonn

%O 1,8

%A _Bianca Newell_, Jun 25 2021

%E Terms a(23) and beyond from _Andrew Howroyd_, Jan 24 2023