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

0,6

Comments

For tiling algorithm, see A351322.

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

Links

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

Example

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

Prog

(Maxima) See A352589.

Crossrefs

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

Main diagonal is A354067.

Cf. A351322, A352589.

Sequence in context: A202875 A203956 A082105 * A230073 A143210 A347672

Adjacent sequences: A353960 A353961 A353962 * A353964 A353965 A353966

Keyword

nonn,tabl

Author

Gerhard Kirchner, May 13 2022

Status

approved