A219975 Number of tilings of an n X n square using straight (3 X 1) trominoes and 2 X 2 tiles.

1, 0, 1, 2, 3, 28, 267, 2744, 66653, 2766100, 141365332, 13305552648, 2149055591278, 493880634209398, 192321197859269019, 124351154502319720238, 122893248485909264026734, 199405053536180281080458422, 527809383857797224536981601752

Offset: 0

Author

Alois P. Heinz, Dec 02 2012

Keywords

• nonn
• more

Examples

			a(4) = 3, because there are 3 tilings of a 4 X 4 square using straight (3 X 1) trominoes and 2 X 2 tiles:
  ._._____.  ._____._.  ._._._._.
  | |_____|  |_____| |  | . | . |
  | | . | |  | | . | |  |___|___|
  |_|___| |  | |___|_|  | . | . |
  |_____|_|  |_|_____|  |___|___|  .
		

Links

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

Crossrefs

Main diagonal of A219967.

Cf. A233807.

Extensions

a(12) from Alois P. Heinz, Sep 24 2014

a(13)-a(18) from Martin Fuller, Apr 09 2025