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

0,2

Comments

Tiling algorithm see A351322.

Links

Table of n, a(n) for n=0..20.

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

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).

Example

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

Prog

(Maxima), see A352589.

Crossrefs

Cf. A351322, A352589, A354130, A354131.

Sequence in context: A230962 A073982 A356644 * A335178 A260347 A140650

Adjacent sequences: A354129 A354130 A354131 * A354133 A354134 A354135

Keyword

nonn,easy

Author

Gerhard Kirchner, May 18 2022

Status

approved