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.

46, 2596, 194834, 15834801, 1395436949, 128352319891, 12224079725173, 1193967045643245, 118973723976420310

Offset: 1

Author

Søren Eilers, Oct 29 2006

Keywords

• nonn
• hard

Comments

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

Examples

			From _Matthias Simon_, Aug 16 2018: (Start)
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:
1) For n=1, the figure is just another LEGO block.
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.
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.
4) Summing up: a(1) = 21 + 25 = 46.
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 ...
a) ... may also be put onto the fixed block (if there are free studs)
b) ... or may be put onto the first additional block.
Following a), 480 figures can be obtained.
Following b), 46^2 = 2116 figures can be obtained.
Summing up: a(2) = 480 + 2116 = 2596.
(End)
		

Crossrefs

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

Formula

a(n) >= 46^n.

Extensions

a(8)-a(9) from Matthias Simon, Aug 14 2018