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

Author

Gerhard Kirchner, May 14 2022

Keywords

• nonn
• easy

Comments

For tiling algorithm, see A351322.

Examples

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

Links

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

Crossrefs

Cf. A351322, A352589, A354010, A354012.

Programs

Maxima

See A352589.

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).