A118649 Row sums for A106597.

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

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

Table of n, a(n) for n=0..28.

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

Cf. A106597.

Sequence in context: A369145 A262320 A062423 * A033482 A054341 A000106

Adjacent sequences: A118646 A118647 A118648 * A118650 A118651 A118652

Keyword

nonn

Author

Joshua Zucker, May 10 2006

Status

approved