A343161 Number of planar distributive lattices with n nodes.

1, 1, 1, 2, 3, 5, 8, 14, 24, 42, 72, 127, 221, 390, 684, 1207, 2125, 3753, 6620, 11698, 20659, 36518, 64533, 114099, 201707, 356683, 630693, 1115370, 1972469, 3488489, 6169656, 10912003, 19299555, 34135099, 60374747, 106786342, 188875933, 334072759, 590889162, 1045136443

Offset: 1

Author

N. J. A. Sloane, Apr 18 2021, following a suggestion from Allan C. Wechsler

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Peter Jipsen, Planar distributive lattices up to size 11, March 2014.
• Peter Jipsen, Planar distributive lattices up to size 15, March 2014.
• Peter Jipsen, Planar vertically indecomposable distributive lattices up to size 22, March 2014.

Crossrefs

Cf. A006966, A006982, A345734.

Programs

PARI

V=concat(digits(1101010214296),[21,18,48,50,114,135,277,358,681]); P=List(1); for(n=2,#V,listput(P,V[2..n]*Colrev(P))); A343161=Vec(P) \\ M. F. Hasler, Jun 22 2021, using V[1..22] & formula from Bianca Newell

PARI

\\ Needs S, V defined in A345734.
seq(n)={Vec(x/(1 - x - Ser((S(n)+V(n))/2)))} \\ Andrew Howroyd, Jan 24 2023

Python

v=[1,1,1,0,1,0,1,0,2,1,4,2,9,6,21,18,48,50,114,135,277,358,681]
p=[1,1,1]
for n in range(3,23):
    p=p+[sum(v[k]*p[n-k+1] for k in range(2,n+1))]
p # Bianca Newell, Jun 22 2021

Formula

a(n) = Sum_{k=2..n} V(k)*a(n-k+1), where V(k) is the number of planar vertically indecomposable distributive lattices of size k. - Bianca Newell, Jun 22 2021

G.f.: x/(2 - B(x)/x) where B(x) is the g.f of A345734. - Andrew Howroyd, Jan 24 2023

Extensions

a(16)-a(22), computed with Python code, from Bianca Newell, Jun 22 2021

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