OFFSET
1,4
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.
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
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 18 2021, following a suggestion from Allan C. Wechsler.
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
STATUS
approved