OFFSET
0,2
COMMENTS
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]
LINKS
S. Kitaev and J. Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.
FORMULA
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]
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joshua Zucker, May 10 2006
STATUS
approved