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

1, 1, 0, 1, 0, 1, 0, 2, 1, 4, 2, 9, 6, 21, 18, 48, 50, 114, 135, 277, 358, 681, 935, 1693, 2425, 4235, 6258, 10643, 16085, 26852, 41226, 67921, 105456, 172125, 269375, 436785, 687409, 1109411, 1752966, 2819711, 4468025, 7170045, 11384240, 18238260, 28999047

Offset: 1

Author

Bianca Newell, Jun 25 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Peter Jipsen, Planar vertically indecomposable distributive lattices up to size 22, March 2014.

Crossrefs

Cf. A072361, A343161.

Programs

PARI

\\ S is symmetric only, V counts reflections separately.
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}
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}
seq(n)={(S(n)+V(n))/2 + vector(n, i, i<=2)} \\ Andrew Howroyd, Jan 24 2023

Extensions

Terms a(23) and beyond from Andrew Howroyd, Jan 24 2023