A219952 Number of tilings of an n X n square using right trominoes and 2 X 2 tiles.

1, 0, 1, 0, 6, 0, 545, 5504, 652036, 44013568, 11112714624, 3517475475328, 2781543486427548, 3568483481372543360, 9829161878198755474915, 48599777948701165162242560, 484370819140388708451108625276, 9036085159101926537420075859958528

Offset

0,5

Links

Table of n, a(n) for n=0..17.

Kai Liang, Solving tiling enumeration problems by tensor network contractions, arXiv:2503.17698 [math.CO], 2025. See p. 25, Table 4.

Example

a(4) = 6, because there are 6 tilings of a 4 X 4 square using right trominoes and 2 X 2 tiles:
  .___.___. .___.___. .___.___. .___.___. .___.___. .___.___.
  | . | . | | ._|_. | | ._| . | | ._|_. | | ._|_. | | . |_. |
  |___|___| |_| . |_| |_| |___| |_| ._|_| |_|_. |_| |___| |_|
  | . | . | | |___| | | |___| | | |_| . | | . |_| | | |___| |
  |___|___| |___|___| |___|___| |___|___| |___|___| |___|___|

Crossrefs

Main diagonal of A219946.

Cf. A233807.

Sequence in context: A111372 A294686 A179936 * A156444 A218343 A122192

Adjacent sequences: A219949 A219950 A219951 * A219953 A219954 A219955

Keyword

nonn

Author

Alois P. Heinz, Dec 01 2012

Extensions

a(15)-a(16) from Alois P. Heinz, Sep 24 2014

a(17) from Alois P. Heinz, Nov 18 2018

Status

approved