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A343161
Number of planar distributive lattices with n nodes.
4
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
1,4
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