A354130 -id:A354130 - cp's OEIS frontend

A354131 Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

1, 2, 12, 48, 216, 936, 4104, 17928, 78408, 342792, 1498824, 6553224, 28652616, 125277192, 547747272, 2394904968, 10471198536, 45783025416, 200176267464, 875226954888, 3826738469448, 16731577137672, 73155162229704, 319854949515144, 1398495821923656

Offset: 0

Gerhard Kirchner, May 18 2022

Tiling algorithm see A351322.

			a(3)=48
Number of tilings without a 2 X 2 square: 44, see A353878.
Number of other tilings: 4
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Index entries for linear recurrences with constant coefficients, signature (3,6).

Cf. A351322, A352589, A353878, A354130, A354132.

Maxima
```
, see A352589.
```

G.f.: (1 - x) / (1 - 3*x - 6*x^2).

a(n) = 3*a(n-1) + 6*a(n-2).

A354132 Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

Original entry on oeis.org

1, 3, 48, 405, 4185, 40320, 397755, 3892293, 38193444, 374425263, 3671810235, 36003770640, 353046480345, 3461866214283, 33946152068808, 332866572321933, 3263999126947497, 32005882711563552, 313840950402409011, 3077438640586986141, 30176522977460549436

Offset: 0

Gerhard Kirchner, May 18 2022

Tiling algorithm see A351322.

			a(2) = 48, see 2 X 3, A354131.

Index entries for linear recurrences with constant coefficients, signature (6,38,0,-68,24,-3).

Cf. A351322, A352589, A354130, A354131.

Maxima
```
, see A352589.
```

G.f.: (1 - 3*x - 8*x^2 + 3*x^3 - x^4) / (1 - 6*x - 38*x^2 + 68*x^4 - 24*x^5 + 3*x^6).

a(n) = 6*a(n-1) + 38*a(n-2) - 68*a(n-4) + 24*a(n-5) - 3*a(n-6).

cp's OEIS Frontend

A354131 Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

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