A123764 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.
1, 2, 7, 24, 99, 416, 1854, 8407, 38970, 182742, 866442, 4140607, 19925401, 96430625, 469005432, 2290860538, 11232074043, 55255074216, 272634835875, 1348823736479, 6689314884962, 33247860759418, 165583649067958, 826170069700588, 4129098732200830
Offset: 1
Links
- M. Abrahamsen and S. Eilers, On the asymptotic enumeration of LEGO structures, Exper. Math. 20 (2) (2011) 145-152.
- B. Durhuus and S. Eilers, Combinatorial aspects of pyramids of one-dimensional pieces of fixed integer length. Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.143-158, 2010, DMTCS Proceedings.
- B. Durhuus and S. Eilers, On the entropy of LEGO, arXiv:math/0504039 [math.CO], 2005; Journal of Applied Mathematics & Computing 45 (2014) 433-448.
- S. Eilers, A LEGO Counting problem, 2005.
- S. Eilers, The LEGO counting problem, Amer. Math. Monthly, 123 (May 2016), 415-426.
- R. Mølck Nilsson, On the number of flat LEGO structures [dead link]. MSc Thesis in mathematics, University of Copenhagen, 2016.
- Index entry for sequences related to LEGO blocks
Formula
Extensions
a(20)-a(25) from Søren Eilers, Sep 12 2018
Comments