A368224 - OEIS

A368224

Table read by antidiagonals: T(n,k) is the number of tilings of the n X k grid up to 180-degree rotation by an asymmetric tile.

1, 3, 3, 4, 10, 4, 10, 36, 36, 10, 16, 136, 256, 136, 16, 36, 528, 2080, 2080, 528, 36, 64, 2080, 16384, 32896, 16384, 2080, 64, 136, 8256, 131328, 524800, 524800, 131328, 8256, 136, 256, 32896, 1048576, 8390656, 16777216, 8390656, 1048576, 32896, 256

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

Peter Kagey, Illustration of T(3,3)=256

Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023.

EXAMPLE

Table begins:

n\k| 1 2 3 4 5 6

---+---------------------------------------------

1 | 1 3 4 10 16 36