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

Author

Gerhard Kirchner, May 18 2022

Keywords

• nonn
• tabl

Comments

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).

Examples

			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
		

Crossrefs

Cf. A000045, A351322, A354131, A354132.

Programs

Maxima

, see A352589.