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? Neil Sloane
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.
On 05/12/05, Jud McCranie <j.mccranie@adelphia.net> wrote:
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.
Google has a cached version of the page (without images, unfortunately, but the text is what matters most anyway): http://216.239.51.104/search?q=cache:FwBG1GLpNgQJ:www.math.ku.dk/~eilers/leg... -- schnee
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.
At 11:15 PM 12/4/2005, Gerald McGarvey wrote:
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.
Yes, I had just found that.
Thanks to everyone who answered my question about Lego blocks. The results are summarized in the two new sequences A112389 and A112390. Neil Sloane
participants (4)
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Gerald McGarvey -
Jud McCranie -
N. J. A. Sloane -
Schneelocke