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A118649 Row sums for A106597.

%I A118649 #25 Jun 05 2025 20:37:41
%S A118649 1,2,5,12,30,74,184,456,1132,2808,6968,17288,42896,106432,264080,
%T A118649 655232,1625760,4033824,10008704,24833536,61616832,152883328,
%U A118649 379333248,941199488,2335298816,5794330112,14376858880,35671780352,88508618240
%N A118649 Row sums for A106597.
%C A118649 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]
%C A118649 From _Sean A. Irvine_, Jun 05 2025: (Start)
%C A118649 Also, the number of walks of length n starting at vertex 2 in the graph:
%C A118649     1-2
%C A118649    /| |
%C A118649   0 | |
%C A118649    \| |
%C A118649     4-3. (End)
%H A118649 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A118649 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 A118649 From _R. J. Mathar_, Nov 10 2009: (Start)
%F A118649 a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3).
%F A118649 G.f.: (1-x^2) / (1-2*x-2*x^2+2*x^3). (End)
%t A118649 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 A118649 Cf. A106597.
%K A118649 nonn
%O A118649 0,2
%A A118649 _Joshua Zucker_, May 10 2006