Lego bricks

[Gerald McGarvey]

The wikipedia information are likely from the article
'On entropy of LEGO' by Bergfinnur Durhuus and Søren Eilers
at arXiv that discusses this. The two figures agree with the article.

http://arxiv.org/PS_cache/math/pdf/0504/0504039.pdf

Some excerpts:
"... 102981500 ... only gives (with a small error, as we shall see) the 
number of ways
to build a tower of LEGO blocks of height six. The total number of 
configurations is
915103765 ...
... letting H_2x4(n,m) denote the number of ways to build a building of 
height m
with n 2 × 4 LEGO blocks ...
... the total number T_2x4(n) of contiguous configurations, counted up to 
symmetry. ..."

 From Figure 3, T_2x4(n) for n=1 to 7 starts as
1, 24, 1560, 119580, 10116403, 915103765, 85747377755

 From Figure 2, the triangle H_2x4(n,m) where the heights m are the columns 
and the number n of
8-stud LEGO bricks (of the same color) are the rows starts (with n starting 
at 2) as
24
500 1060
11707 59201 48672
248688 3203175 4425804 2238736
7946227 162216127 359949655 282010252 102981504

Regards,
Gerald McGarvey


At 10:35 PM 12/4/2005, Jud McCranie wrote:
>At 09:16 PM 12/4/2005, N. J. A. Sloane wrote:
>>The New Yorker for Apr 27/May 4 1998 has an article
>>by Anthony Lane, The Joy of Bricks, where he says
>>that there are 102981500 ways to combine 6 Lego pieces.
>>This is a sequence that appears to be missing from the OEIS.
>>Can anyone supply the earlier terms?
>
>
>http://en.wikipedia.org/wiki/Lego lists 915,103,765 for six and 1560 for 
>three.  (The link there is dead.)  I'll look for it.
>
>
>