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

0,5

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).

Links

Table of n, a(n) for n=0..35.

Example

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

Prog

(Maxima), see A352589.

Crossrefs

Cf. A000045, A351322, A354131, A354132.

Sequence in context: A287704 A351456 A082185 * A113491 A107773 A221075

Adjacent sequences: A354127 A354128 A354129 * A354131 A354132 A354133

Keyword

nonn,tabl

Author

Gerhard Kirchner, May 18 2022

Status

approved