A353963 Triangle read by rows: T(n,k) = number of tilings of a n X k rectangle using 2 X 2 and 1 X 1 tiles and right trominoes, n >= 0, k=0..n.

1, 1, 1, 1, 1, 6, 1, 1, 13, 47, 1, 1, 45, 259, 3376, 1, 1, 122, 1189, 29683, 475962, 1, 1, 373, 5877, 311894, 9250945, 355724934, 1, 1, 1073, 28167, 3015423, 164776003, 12126673297, 777719132265, 1, 1, 3182, 136723, 30295051, 3051272172, 436744432876, 53090133270415, 6953251175836902

Offset: 0

Author

Gerhard Kirchner, May 13 2022

Keywords

• nonn
• tabl

Comments

For tiling algorithm, see A351322.

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

Examples

			Triangle begins
  n\k  0 1   2    3      4       5         6
  ------------------------------------------
  0:   1
  1:   1 1
  2:   1 1   6
  3:   1 1  13   47
  4:   1 1  45  259   3376
  5:   1 1 122 1189  29683  475962
  6:   1 1 373 5877 311894 9250945 355724934
		

Links

• Liang Kai, Rows n=0..17 of triangle, flattened

Crossrefs

Row/columns 0..3 are A000012, A000012, A353964, A353965.

Main diagonal is A354067.

Cf. A351322, A352589.

Programs

Maxima

See A352589.