A123765 - OEIS

A123765

Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 1 X 2 which is flat, i.e., with all blocks in parallel position and symmetric after a rotation by 180 degrees.

%I #24 May 30 2026 16:40:31

%S 1,1,3,4,12,18,52,83,235,389,1087,1851,5113,8891,24357,43045,117127,

%T 209731,567487,1027245,2766404,5053521,13554315,24954627,66696366,

%U 123628610,329400200,614216837,1632039074,3059240151,8108703876

%N Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 1 X 2 which is flat, i.e., with all blocks in parallel position and symmetric after a rotation by 180 degrees.

%H M. Abrahamsen and S. Eilers, <a href="https://doi.org/10.1080/10586458.2011.564539">On the asymptotic enumeration of LEGO structures</a>, Exper Math. 20 (2) (2011) 145-152.

%H B. Durhuus and S. Eilers, <a href="https://arxiv.org/abs/math/0504039">On the entropy of LEGO</a>, arXiv:math.CO/0504039

%H S. Eilers, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.123.5.415">The LEGO counting problem</a>, Amer. Math. Monthly, 123 (May 2016), 415-426.

%H <a href="/wiki/Index_to_OEIS:_Section_Lc#LEGO">Index entry for sequences related to LEGO blocks</a>

%K nonn,more

%O 1,3

%A _Søren Eilers_, Oct 29 2006

%E More terms by _Søren Eilers_, Sep 12 2018