login
Number of stable towers of 2 X 2 LEGO blocks.
(Formerly M2675)
2

%I M2675 #32 Feb 24 2020 21:56:10

%S 1,3,7,19,53,149,419,1191,3403,9755,28077,81097,234861,681697,1982723,

%T 5777375,16861521,49281525,144222987,422566835,1239423303,3638872529,

%U 10693065215,31448140529,92558787745,272612601065,803448576111

%N Number of stable towers of 2 X 2 LEGO blocks.

%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27.

%H Ray Chandler, <a href="/A007575/b007575.txt">Table of n, a(n) for n = 0..2098</a> (terms < 10^1000)

%H 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 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 <a href="/wiki/Index_to_OEIS:_Section_Lc#LEGO">Index entry for sequences related to LEGO blocks</a>

%F a(n) ~ 3^(n+1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jul 11 2018

%p 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 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 Cf. A007576.

%K nonn

%O 0,2

%A _Simon Plouffe_ and _N. J. A. Sloane_, _Robert G. Wilson v_