This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123830 #20 Aug 17 2018 10:58:57 %S A123830 46,2596,194834,15834801,1395436949,128352319891,12224079725173, %T A123830 1193967045643245,118973723976420310 %N A123830 Number of ways to build a contiguous building with n LEGO blocks of size 2 X 4 on top of a fixed block of the same size. %C A123830 The base block is not counted among the n and must be the only block in the bottom layer of the building. %F A123830 a(n) >= 46^n. %e A123830 From _Matthias Simon_, Aug 16 2018: (Start) %e A123830 Explanation to a(1): There is a 2 X 4 LEGO block fixed at the ground. There are 46 ways to put a building consisting of n=1 LEGO block onto the fixed block, because: %e A123830 1) For n=1, the figure is just another LEGO block. %e A123830 2) If the two LEGO blocks are parallel, the upper LEGO block can be shifted in 3*7 = 21 different ways relatively to the lower one. %e A123830 3) If the LEGO blocks are in a right angle to each other, the upper LEGO block can be shifted in 5*5 = 25 different ways relatively to the lower one. %e A123830 4) Summing up: a(1) = 21 + 25 = 46. %e A123830 Explanations to a(2): Two additional LEGO blocks are added to a fixed one. The first additional block is put onto the fixed one, the second additional block ... %e A123830 a) ... may also be put onto the fixed block (if there are free studs) %e A123830 b) ... or may be put onto the first additional block. %e A123830 Following a), 480 figures can be obtained. %e A123830 Following b), 46^2 = 2116 figures can be obtained. %e A123830 Summing up: a(2) = 480 + 2116 = 2596. %e A123830 (End) %Y A123830 Cf. A112389, A123762 - A123827, A123829 - A123849. %K A123830 nonn,hard %O A123830 1,1 %A A123830 _Søren Eilers_, Oct 29 2006 %E A123830 a(8)-a(9) from _Matthias Simon_, Aug 14 2018