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A123764
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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The exponential growth is estimated to be 5.203 in Mølck Nilsson's MSc thesis. This puts an end to the speculation that it may be 5 at the end of the paper "Combinatorial aspects of pyramids of one-dimensional pieces of fixed integer length" by Durhuus and Eilers.
a(20)-a(25) follow from Rasmus Mølck Nilsson's extension of A319156 by transfer-matrix methods. (End)
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LINKS
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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.
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FORMULA
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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