A007575 Number of stable towers of 2 X 2 LEGO blocks.
1, 3, 7, 19, 53, 149, 419, 1191, 3403, 9755, 28077, 81097, 234861, 681697, 1982723, 5777375, 16861521, 49281525, 144222987, 422566835, 1239423303, 3638872529, 10693065215, 31448140529, 92558787745, 272612601065, 803448576111
Offset: 0
Keywords
References
- Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27.
Links
- Ray Chandler, Table of n, a(n) for n = 0..2098 (terms < 10^1000)
- Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Laboratoire d'Informatique de Paris Nord (LIPN 2019).
- P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27. (Annotated scanned copy)
- Index entry for sequences related to LEGO blocks
Crossrefs
Cf. A007576.
Programs
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Maple
seq(sum(coeff(product(1+x^k+x^(2*k),k=1..n),x,l),l=n*(n+1)/2-n..n*(n+1)/2+n),n=0..20); # Søren Eilers
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Mathematica
Array[Sum[SeriesCoefficient[Product[1 + x^k + x^(2 k), {k, #}], {x, 0, j}], {j, # (# + 1)/2 - #, # (# + 1)/2 + #}] &, 27, 0] (* Michael De Vlieger, Feb 24 2020, after Maple *)
Formula
a(n) ~ 3^(n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2018