A353877 Triangle read by rows: T(k,n) (k >= 0, n = 0, ..., k) = number of tilings of a k X n rectangle using right trominoes, dominoes and 1 X 1 tiles.

1, 1, 1, 1, 2, 11, 1, 3, 44, 369, 1, 5, 189, 3633, 83374, 1, 8, 798, 34002, 1817897, 90916452, 1, 13, 3383, 323293, 40220893, 4635661331, 546063639624, 1, 21, 14328, 3058623, 886130549, 235025597912, 63919977468729, 17259079054003609, 1, 34, 60697, 28982628, 19546906987, 11935601703140, 7495901454256347, 4669873251135795702, 2916019543694306398589

Offset

0,5

Comments

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) = A000045(n+1), Fibonacci numbers.

T(2,n) = A110679(n), T(3,n) = A353878(n), T(4,n) = A353879(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  2   11
3:  1  3   44    369
4:  1  5  189   3633    83374
5:  1  8  798  34002  1817897   90916452
6:  1 13 3383 323293 40220893 4635661331 546063639624

Prog

(Maxima) See A352589.

Crossrefs

Cf. A000045, A110679, A219987, A351322, A352589, A353878, A353879.

T(n,n) gives A353934.

Sequence in context: A057213 A326042 A350035 * A250221 A365610 A298444

Adjacent sequences: A353874 A353875 A353876 * A353878 A353879 A353880

Keyword

nonn,tabl

Author

Gerhard Kirchner, May 09 2022

Status

approved