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

0,6

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).

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 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

Prog

(Maxima) See A352589.

Crossrefs

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

T(n,n) gives A354119.

Sequence in context: A111246 A206306 A178124 * A143395 A090536 A187557

Adjacent sequences: A354007 A354008 A354009 * A354011 A354012 A354013

Keyword

nonn,tabl

Author

Gerhard Kirchner, May 14 2022

Status

approved