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

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

0,3

Comments

For tiling algorithm, see A351322.

Links

Table of n, a(n) for n=0..26.

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

Formula

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).

Example

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

Prog

(Maxima) See A352589.

Crossrefs

Cf. A351322, A352589, A354010, A354012.

Sequence in context: A251626 A256340 A192373 * A103680 A219518 A029496

Adjacent sequences: A354008 A354009 A354010 * A354012 A354013 A354014

Keyword

nonn,easy

Author

Gerhard Kirchner, May 14 2022

Status

approved