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Triangle read by rows: T(n,k) is the number of ways of building a building of height k using n 2 X 4 LEGO blocks, counted up to symmetry (for 2 <= k <= n).
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%I #26 Jun 01 2024 11:14:23

%S 24,500,1060,11707,59201,48672,248688,3203175,4425804,2238736,7946227,

%T 162216127,359949655,282010252,102981504

%N Triangle read by rows: T(n,k) is the number of ways of building a building of height k using n 2 X 4 LEGO blocks, counted up to symmetry (for 2 <= k <= n).

%D Anthony Lane, The Joy of Bricks, The New Yorker, Apr 27-May 04, 1998, pp. 96-103.

%H B. Durhuus and S. Eilers, <a href="https://arxiv.org/abs/math/0504039">On entropy of LEGO</a>, arXiv:math/0504039 [math.CO], 2005.

%H S. Eilers, <a href="http://www.math.ku.dk/~eilers/lego.html">A LEGO Counting problem</a>.

%H <a href="/wiki/Index_to_OEIS:_Section_Lc#LEGO">Index entry for sequences related to LEGO blocks</a>.

%e Triangle begins:

%e 24;

%e 500, 1060;

%e 11707, 59201, 48672;

%e 248688, 3203175, 4425804, 2238736;

%e 7946227, 162216127, 359949655, 282010252, 102981504;

%Y Cf. A112389.

%K nonn,tabl,more

%O 2,1

%A _N. J. A. Sloane_, Dec 06 2005

%E Thanks to _Gerald McGarvey_, _Christian Schroeder_ and _Jud McCranie_, who contributed to this entry.