



1, 2, 5, 12, 30, 74, 184, 456, 1132, 2808, 6968, 17288, 42896, 106432, 264080, 655232, 1625760, 4033824, 10008704, 24833536, 61616832, 152883328, 379333248, 941199488, 2335298816, 5794330112, 14376858880, 35671780352, 88508618240
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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 n1 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]}. [From Emilie Hogan, Oct 16 2009]


LINKS

Table of n, a(n) for n=0..28.
S. Kitaev, J. Remmel, (a,b)rectangle patterns in permutations and words, arXiv:1304.4286


FORMULA

Conjecture: a(n)=2*a(n1)+2*a(n2)2*a(n3) with g.f. (1x^2)/(12*x2*x^2+2*x^3). [From 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] (* JeanFrançois Alcover, Oct 30 2018, after Emanuele Munarini in A106597 *)


CROSSREFS

Sequence in context: A046170 A262320 A062423 * A033482 A054341 A000106
Adjacent sequences: A118646 A118647 A118648 * A118650 A118651 A118652


KEYWORD

nonn


AUTHOR

Joshua Zucker, May 10 2006


STATUS

approved



