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

Author

Christian G. Bower, Dec 28 2000

Keywords

• nonn
• hard
• more

References

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

Links

• 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

Crossrefs

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

Programs

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 *)

Extensions

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