A354012 -id:A354012 - cp's OEIS frontend

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

Gerhard Kirchner, May 14 2022

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).

			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

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

T(n,n) gives A354119.

Maxima
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See A352589.
```

A354011 Number of tilings of a 3 X n rectangle using 2 X 2 tiles, right trominoes and dominoes.

Original entry on oeis.org

1, 0, 7, 8, 81, 184, 1051, 3176, 14609, 50408, 210903, 773888, 3102369, 11711856, 46045259, 176114128, 686258465, 2640610128, 10247733223, 39540368248, 153162778865, 591718044968, 2290106238779, 8852558325048, 34248315785777, 132424316290104, 512224146701367

Offset: 0

Gerhard Kirchner, May 14 2022

For tiling algorithm, see A351322.

			a(2)=7:
   ___    ___    ___    ___    ___    ___    ___
  |   |  |___|  |_  |  |  _|  |___|  |___|  |_|_|
  |___|  |   |  | |_|  |_| |  |___|  |_|_|  |_|_|
  |___|  |___|  |___|  |___|  |___|  |_|_|  |___|

Index entries for linear recurrences with constant coefficients, signature (2,9,-8,3,6,-3).

Cf. A351322, A352589, A354010, A354012.

Maxima
```
See A352589.
```

G.f.: (1 - 2*x - 2*x^2 + 2*x^3 - x^4) / (1 - 2*x - 9*x^2 + 8*x^3 - 3*x^4 - 6*x^5 + 3*x^6).

a(n)=2*a(n-1) + 9*a(n-2) - 8*a(n-3) + 3*a(n-4) + 6*a(n-5) - 3*a(n-6).

cp's OEIS Frontend

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.

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