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A007575 Number of stable towers of 2 X 2 LEGO blocks.

%I A007575 M2675 #32 Feb 24 2020 21:56:10
%S A007575 1,3,7,19,53,149,419,1191,3403,9755,28077,81097,234861,681697,1982723,
%T A007575 5777375,16861521,49281525,144222987,422566835,1239423303,3638872529,
%U A007575 10693065215,31448140529,92558787745,272612601065,803448576111
%N A007575 Number of stable towers of 2 X 2 LEGO blocks.
%D A007575 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.
%D A007575 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007575 P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27.
%H A007575 Ray Chandler, <a href="/A007575/b007575.txt">Table of n, a(n) for n = 0..2098</a> (terms < 10^1000)
%H A007575 Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/patterns2019.pdf">Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata</a>, Laboratoire d'Informatique de Paris Nord (LIPN 2019).
%H A007575 P. J. S. Watson, <a href="/A007575/a007575.pdf">On "LEGO" towers</a>, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27. (Annotated scanned copy)
%H A007575 <a href="/wiki/Index_to_OEIS:_Section_Lc#LEGO">Index entry for sequences related to LEGO blocks</a>
%F A007575 a(n) ~ 3^(n+1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jul 11 2018
%p A007575 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_
%t A007575 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 *)
%Y A007575 Cf. A007576.
%K A007575 nonn
%O A007575 0,2
%A A007575 _Simon Plouffe_ and _N. J. A. Sloane_, _Robert G. Wilson v_