A354132 Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

1, 3, 48, 405, 4185, 40320, 397755, 3892293, 38193444, 374425263, 3671810235, 36003770640, 353046480345, 3461866214283, 33946152068808, 332866572321933, 3263999126947497, 32005882711563552, 313840950402409011, 3077438640586986141, 30176522977460549436

Offset: 0

Author

Gerhard Kirchner, May 18 2022

Keywords

• nonn
• easy

Comments

Tiling algorithm see A351322.

Examples

			a(2) = 48, see 2 X 3, A354131.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,38,0,-68,24,-3).

Crossrefs

Cf. A351322, A352589, A354130, A354131.

Programs

Maxima

, see A352589.

Formula

G.f.: (1 - 3*x - 8*x^2 + 3*x^3 - x^4) / (1 - 6*x - 38*x^2 + 68*x^4 - 24*x^5 + 3*x^6).

a(n) = 6*a(n-1) + 38*a(n-2) - 68*a(n-4) + 24*a(n-5) - 3*a(n-6).