A123769 Number of ways to build a contiguous building with n LEGO blocks of size 1 X 2 on top of a fixed block of the same size so that the building is flat, i.e., with all blocks in parallel position and symmetric after a rotation by 180 degrees.

1, 2, 3, 6, 11, 23, 43, 93, 181, 392, 783, 1710, 3467, 7623, 15655, 34543, 71688, 158721, 332006, 737213, 1552365, 3455004, 7315948, 16315297, 34711474, 77544359, 165653643, 370623055

Offset

1,2

Comments

The base block is not counted among the n and must be the only block in the bottom layer of the building.

Links

Table of n, a(n) for n=1..28.

M. Abrahamsen and S. Eilers, On the asymptotic enumeration of LEGO structures, Exper Math. 20 (2) (2011) 145-152.

B. Durhuus and S. Eilers, On the entropy of LEGO, arXiv:math/0504039 [math.CO], 2005.

S. Eilers, The LEGO counting problem, Amer. Math. Monthly, 123 (May 2016), 415-426.

Index entry for sequences related to LEGO blocks

Crossrefs

Sequence in context: A036653 A318031 A316500 * A093304 A036590 A247139

Adjacent sequences: A123766 A123767 A123768 * A123770 A123771 A123772

Keyword

nonn,more

Author

Søren Eilers, Oct 29 2006

Extensions

a(21)-a(28) from Søren Eilers, Sep 16 2018

Status

approved