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A030268 Number of nonisomorphic connected partial lattices. 1
1, 1, 1, 3, 9, 35, 153, 791, 4597, 29988, 215804, 1697291, 14457059, 132392971, 1295346365, 13468653637, 148142236784, 1716782858995, 20889118889021 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A partial lattice is a poset where every pair of points has a unique least upper (greatest lower) bound or has no upper (lower) bound.

LINKS

Table of n, a(n) for n=0..18.

N. J. A. Sloane, Transforms

FORMULA

Inverse Euler transform of A006966(n-2) (lattices).

MATHEMATICA

A006966 = DeleteCases[Import["https://oeis.org/A006966/b006966.txt", "Table"], {}][[All, 2]];

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

EULERi[b_List] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

Join[{1}, EULERi[Drop[A006966, 3]]] (* Jean-François Alcover, May 10 2019 *)

CROSSREFS

Sequence in context: A327885 A074507 A217924 * A097277 A034428 A101880

Adjacent sequences:  A030265 A030266 A030267 * A030269 A030270 A030271

KEYWORD

nonn,hard

AUTHOR

Christian G. Bower, revised Dec 28 2000

EXTENSIONS

a(17) (from A006966) from Jean-François Alcover, May 10 2019

a(18) (using A006966) from Alois P. Heinz, May 10 2019

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)