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%I #18 Sep 08 2021 03:43:04
%S 1,2,5,12,30,74,184,456,1132,2808,6968,17288,42896,106432,264080,
%T 655232,1625760,4033824,10008704,24833536,61616832,152883328,
%U 379333248,941199488,2335298816,5794330112,14376858880,35671780352,88508618240
%N Row sums for A106597.
%C For n>=2, a(n)= Number of "stable LEGO walls" (i.e., walls in which seams don't match up from one level to the next) of width 7 and height n-1 when using bricks of length 2, 3, and 4. For example, there are a(2)=5 stable LEGO walls of height 1 and they are {[2,2,3],[2,3,2],[3,2,2],[3,4],[4,3]}. [_Emilie Hogan_, Oct 16 2009]
%H S. Kitaev and J. Remmel, <a href="http://arxiv.org/abs/1304.4286">(a,b)-rectangle patterns in permutations and words</a>, arXiv:1304.4286 [math.CO], 2013.
%F Conjecture: a(n) = 2*a(n-1)+2*a(n-2)-2*a(n-3) with g.f. (1-x^2)/(1-2*x-2*x^2+2*x^3). [_R. J. Mathar_, Nov 10 2009]
%t Total[CoefficientList[#, y]]& /@ CoefficientList[(1 - x^2 y)/(1 - x - x y - 2 x^2 y + x^3 y + x^3 y^2) + O[x]^29, x] (* _Jean-François Alcover_, Oct 30 2018, after _Emanuele Munarini_ in A106597 *)
%Y Cf. A106597.
%K nonn
%O 0,2
%A _Joshua Zucker_, May 10 2006
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