A342132 Number of unlabeled vertically indecomposable modular lattices on n nodes.

1, 1, 0, 1, 1, 2, 3, 7, 12, 28, 54, 127, 266, 614, 1356, 3134, 7091, 16482, 37929, 88622, 206295, 484445, 1136897, 2682451, 6333249, 15005945, 35595805, 84649515, 201560350, 480845007, 1148537092, 2747477575, 6579923491, 15777658535, 37871501929

Offset

1,6

Comments

A lattice is vertically decomposable if it has an element that is comparable to all elements and is neither the bottom nor the top element. Otherwise the lattice is vertically indecomposable.

Links

Table of n, a(n) for n=1..35.

P. Jipsen and N. Lawless, Generating all finite modular lattices of a given size, Algebra universalis, 74 (2015), 253-264.

J. Kohonen, Generating modular lattices of up to 30 elements, Order, 36 (2019), 423-435.

J. Kohonen, Cartesian lattice counting by the vertical 2-sum, arXiv:2007.03232 [math.CO] preprint (2020).

Example

a(7)=3: These are the three lattices.
      o        o         __o__
     / \      /|\       / /|\ \
    o   o    o o o     o o o o o
   /|\ /    / \|/       \_\|/_/
  o o o    o   o           o
   \|/      \ /
    o        o

Crossrefs

Cf. A006981 (modular lattices, including vertically decomposable).

Sequence in context: A296517 A182692 A203837 * A032173 A130616 A089324

Adjacent sequences: A342129 A342130 A342131 * A342133 A342134 A342135

Keyword

nonn

Author

Jukka Kohonen, Mar 01 2021

Status

approved