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A345734 Number of planar vertically indecomposable distributive lattices with n nodes.

%I A345734 #15 Jan 24 2023 23:12:42
%S A345734 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 A345734 2425,4235,6258,10643,16085,26852,41226,67921,105456,172125,269375,
%U A345734 436785,687409,1109411,1752966,2819711,4468025,7170045,11384240,18238260,28999047
%N A345734 Number of planar vertically indecomposable distributive lattices with n nodes.
%H A345734 Andrew Howroyd, <a href="/A345734/b345734.txt">Table of n, a(n) for n = 1..1000</a>
%H A345734 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 A345734 (PARI) \\ S is symmetric only, V counts reflections separately.
%o A345734 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 A345734 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 A345734 seq(n)={(S(n)+V(n))/2 + vector(n, i, i<=2)} \\ _Andrew Howroyd_, Jan 24 2023
%Y A345734 Cf. A072361, A343161.
%K A345734 nonn
%O A345734 1,8
%A A345734 _Bianca Newell_, Jun 25 2021
%E A345734 Terms a(23) and beyond from _Andrew Howroyd_, Jan 24 2023