A354131 -id:A354131 - cp's OEIS frontend

A354130 Triangle read by rows: T(k,n) (k >= 0, n = 0, ..., k) = number of tilings of a k X n rectangle using 2 X 2, and 1 X 1 tiles, right trominoes and dominoes.

1, 1, 1, 1, 2, 12, 1, 3, 48, 405, 1, 5, 216, 4185, 103300, 1, 8, 936, 40320, 2352830, 124098498, 1, 13, 4104, 397755, 55004286, 6763987198, 863829618636, 1, 21, 17928, 3892293, 1274945897, 364713815832, 108969107997657, 32100965172272499

Offset: 0

Gerhard Kirchner, May 18 2022

Tiling algorithm, see A351322.
Reading the sequence {T(k,n)} for n>k, use T(n,k) instead of T(k,n).
T(1,n) = A000045(n+1), Fibonacci numbers.
T(2,n) = A354131(n), T(3,n) = A354132(n).

			Triangle begins
k\n_0__1____2______3________4__________5____________6
0:  1
1:  1  1
2:  1  2   12
3:  1  3   48    405
4:  1  5  216   4185   103300
5:  1  8  936  40320  2352830  124098498
6:  1 13 4104 397755 55004286 6763987198 863829618636

Cf. A000045, A351322, A354131, A354132.

Maxima
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, see A352589.
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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

A354130 Triangle read by rows: T(k,n) (k >= 0, n = 0, ..., k) = number of tilings of a k X n rectangle using 2 X 2, and 1 X 1 tiles, right trominoes and dominoes.

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