A354010 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 tiles, right trominoes and dominoes.

1, 1, 0, 1, 1, 3, 1, 0, 7, 8, 1, 1, 17, 81, 702, 1, 0, 41, 184, 4623, 41952, 1, 1, 99, 1051, 35044, 654673, 16600824, 1, 0, 239, 3176, 248045, 7407376, 358635313, 13298557992, 1, 1, 577, 14609, 1819731, 100694199, 8448412164, 569631442289, 43157780553934

Offset: 0

Author

Gerhard Kirchner, May 14 2022

Keywords

• nonn
• tabl

Comments

For tiling algorithm, see A351322.

Reading the sequence {T(k,n)}, use T(n,k) instead of T(k,n) for n>k.

T(1,n) = A000035(n+1) = (n+1) mod 2,

T(2,n) = A001333(n), T(3,n) = A354011(n), T(4,n) = A354012(n).

Examples

			Triangle begins
  k\n 0 1   2    3      4       5         6
  -----------------------------------------
  0   1
  1   1 0
  2   1 1   3
  3   1 0   7    8
  4   1 1  17   81    702
  5   1 0  41  184   4623   41952
  6   1 1  99 1051  35044  654673  16600824
		

Crossrefs

Cf. A000035, A001333, A351322, A352589, A354011, A354012.

T(n,n) gives A354119.

Programs

Maxima

See A352589.