A058800 Vertically indecomposable lattices on n unlabeled nodes.

1, 1, 1, 0, 1, 2, 7, 27, 126, 664, 3954, 26190, 190754, 1514332, 12998035, 119803771, 1178740932, 12316480222, 136060611189, 1582930919092, 19328253734491

Offset

0,6

References

J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.

Links

Table of n, a(n) for n=0..20.

V. Gebhardt and S. Tawn, Constructing unlabelled lattices, arXiv:1609.08255 [math.CO], 2016.

J. Heitzig and J. Reinhold, Counting finite lattices, preprint no. 298, Institut für Mathematik, Universität Hannover, Germany, 1999.

N. J. A. Sloane, Transforms

Mathematica

A006966 = Cases[Import["https://oeis.org/A006966/b006966.txt", "Table"], {_, _}][[All, 2]];
nmax = Length[A006966] - 1;
B[x_] = Sum[A006966[[n + 1]] x^n, {n, 0, nmax}];
A[x_] = Sum[c[n] x^n, {n, 0, nmax}];
sol = CoefficientList[1 + A[x] - 1/(1 - B[x]) + O[x]^nmax, x] == 0 // Solve // First // Rest // Quiet;
a[n_] := If[n <= 2, 1, c[n - 2] /. sol];
a /@ Range[0, nmax] (* Jean-François Alcover, Dec 05 2019 *)

Crossrefs

a(n+1) is Inverse INVERT transform of A006966(n+1).

Sequence in context: A060017 A211475 A213226 * A357901 A342056 A363199

Adjacent sequences: A058797 A058798 A058799 * A058801 A058802 A058803

Keyword

nonn,hard,more

Author

Christian G. Bower, Dec 28 2000

Extensions

a(19) (computed by Jipsen and Lawless) and a(20) from Volker Gebhardt, Sep 28 2016

Status

approved