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

Author

Joshua Zucker, May 10 2006

Keywords

• nonn

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]

From Sean A. Irvine, Jun 05 2025: (Start)

Also, the number of walks of length n starting at vertex 2 in the graph:

1-2

/| |

0 | |

\| |

4-3. (End)

Links

• Sean A. Irvine, Walks on Graphs.
• S. Kitaev and J. Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.

Crossrefs

Cf. A106597.

Programs

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 *)

Formula

From R. J. Mathar, Nov 10 2009: (Start)

a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3).

G.f.: (1-x^2) / (1-2*x-2*x^2+2*x^3). (End)