%I #12 Apr 18 2021 01:46:43

%S 1,1,0,1,1,2,3,7,12,28,54,127,266,614,1356,3134,7091,16482,37929,

%T 88622,206295,484445,1136897,2682451,6333249,15005945,35595805,

%U 84649515,201560350,480845007,1148537092,2747477575,6579923491,15777658535,37871501929

%N Number of unlabeled vertically indecomposable modular lattices on n nodes.

%C 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.

%H P. Jipsen and N. Lawless, <a href="https://doi.org/10.1007/s00012-015-0348-x">Generating all finite modular lattices of a given size</a>, Algebra universalis, 74 (2015), 253-264.

%H J. Kohonen, <a href="https://doi.org/10.1007/s11083-018-9475-2">Generating modular lattices of up to 30 elements</a>, Order, 36 (2019), 423-435.

%H J. Kohonen, <a href="https://arxiv.org/abs/2007.03232">Cartesian lattice counting by the vertical 2-sum</a>, arXiv:2007.03232 [math.CO] preprint (2020).

%e a(7)=3: These are the three lattices.

%e o o __o__

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

%K nonn

%O 1,6

%A _Jukka Kohonen_, Mar 01 2021