A219874 Number of tilings of an n X n square using dominoes and straight (3 X 1) trominoes.

1, 0, 2, 14, 184, 9612, 1143834, 354859954, 295743829064, 631206895803116, 3541054185616706122, 51821077154605344550820, 1976225122734369352127065686, 196913655491597719598898811003348, 51179690353659852099434654264900753288, 34716223657627061096793572212632925410608268

Offset: 0

Author

Alois P. Heinz, Nov 30 2012

Keywords

• nonn

Examples

			a(3) = 14, because there are 14 tilings of a 3 X 3 square using dominoes and straight (3 X 1) trominoes:
  ._____. ._____. ._____. ._____. .___._. .___._. .___._.
  | | | | | | | | | |___| | |___| | | | | |___| | |___| |
  | | | | | |_|_| | |___| | | | | |_|_| | |___| | | | | |
  |_|_|_| |_|___| |_|___| |_|_|_| |___|_| |___|_| |_|_|_|
  ._____. ._____. ._____. ._____. ._____. ._____. ._____.
  |_____| |_____| |_____| |_____| | |___| | | | | |___| |
  |_____| | |___| | | | | |___| | |_|___| |_|_|_| |___|_|
  |_____| |_|___| |_|_|_| |___|_| |_____| |_____| |_____|  .
		

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 A219866.

Cf. A233807, A364504.

Extensions

a(12) from Alois P. Heinz, Sep 30 2014

a(13)-a(15) (using Liang Kai's terms in A219866) from Alois P. Heinz, Mar 12 2025