Journal of Integer Sequences, Vol. 24 (2021), Article 21.4.5

Tiling a 2 × n Board with Dominos and L-Shaped Trominos


Gregory Dresden
Department of Mathematics
Washington & Lee University
Lexington, VA 24450
USA

Michael Tulskikh
East Mountain High School
Sandia Park, NM 87047
USA

Abstract:

We count the number of ways to tile 2 × n rectangles and bracelets using dominos and L-shaped trominos. We show that these 2 × n tilings can be related to 1 × n tilings with squares, dominos, and two colors of k-minos for k ≥ 3, and we discover some new identities for old sequences.

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(Concerned with sequences A000129 A000133 A001333 A026150 A030186 A052980 A077917 A080204 A097075 A097076 A278815 A332647.)

Received January 18 2021; revised version received April 12 2021. Published in Journal of Integer Sequences, April 16 2021.

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