A123830 - OEIS

%I #20 Aug 17 2018 10:58:57

%S 46,2596,194834,15834801,1395436949,128352319891,12224079725173,

%T 1193967045643245,118973723976420310

%N 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 The base block is not counted among the n and must be the only block in the bottom layer of the building.

%F a(n) >= 46^n.

%e From _Matthias Simon_, Aug 16 2018: (Start)

%e 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 1) For n=1, the figure is just another LEGO block.

%e 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 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 4) Summing up: a(1) = 21 + 25 = 46.

%e 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 a) ... may also be put onto the fixed block (if there are free studs)

%e b) ... or may be put onto the first additional block.

%e Following a), 480 figures can be obtained.

%e Following b), 46^2 = 2116 figures can be obtained.

%e Summing up: a(2) = 480 + 2116 = 2596.

%e (End)

%Y Cf. A112389, A123762 - A123827, A123829 - A123849.

%K nonn,hard

%O 1,1

%A _Søren Eilers_, Oct 29 2006

%E a(8)-a(9) from _Matthias Simon_, Aug 14 2018