A353963 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 and right trominoes.

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(k,n)} for n>k, use T(n,k) instead of T(k,n).

T(1,n) = A000012(n) = constant 1,

T(2,n) = A353964(n), T(3,n) = A353965(n).

Links

Table of n, a(n) for n=0..44.

Example

Triangle begins
  k\n  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

Cf. A000012, A351322, A352589, A353964, A353965.

T(n,n) gives A354067.

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