A354131 Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

1, 2, 12, 48, 216, 936, 4104, 17928, 78408, 342792, 1498824, 6553224, 28652616, 125277192, 547747272, 2394904968, 10471198536, 45783025416, 200176267464, 875226954888, 3826738469448, 16731577137672, 73155162229704, 319854949515144, 1398495821923656

Offset

0,2

Comments

Tiling algorithm see A351322.

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,6).

Formula

G.f.: (1 - x) / (1 - 3*x - 6*x^2).

a(n) = 3*a(n-1) + 6*a(n-2).

Example

a(3)=48
Number of tilings without a 2 X 2 square: 44, see A353878.
Number of other tilings: 4
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Prog

(Maxima), see A352589.

Crossrefs

Cf. A351322, A352589, A353878, A354130, A354132.

Sequence in context: A001815 A347324 A333728 * A370696 A052569 A221663

Adjacent sequences: A354128 A354129 A354130 * A354132 A354133 A354134

Keyword

nonn,easy

Author

Gerhard Kirchner, May 18 2022

Status

approved