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

Author

Jukka Kohonen, Mar 01 2021

Keywords

• nonn

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.

Examples

			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
		

Links

• 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).

Crossrefs

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