A386222 Number of 3-dimensional tilings of a 2 X 2 X (n+1) box with the two upper right cells removed, using 2 X 2 X 1 plates and 1 X 2 X 1 dominos.

1, 5, 34, 201, 1241, 7538, 46045, 280693, 1712338, 10443297, 63697825, 388506066, 2369604597, 14452808029, 88151396594, 537657790873, 3279312211305, 20001361622066, 121993408939853, 744068928339589, 4538266259447698, 27680043927136849, 168827650973959281

Offset: 0

Author

Greg Dresden and Xiaoya Gao, Aug 13 2025

Keywords

• nonn
• changed

Comments

Here is the box for n=3:

__________

/ / / /|

/_/___/_/ |__

/ / / /| / /|

/_/___/_/ |/_/ |

| | | | / /| /

|_|___|_|/_/ |/

| | | | | /

|_|___|_|___| /.

Examples

			Here is one of the a(1)=5 ways to tile the shape for n=1, in this case with one flat plate on the bottom and one domino on top.
    ____
   /   /|
  /   / |____
 /   /  /   /|
/___/  /   / |
|   | /   /  /
|___|/___/  /
|       |  /
|_______| /.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,9,-14).

Crossrefs

Cf. A359884

Programs

Mathematica

LinearRecurrence[{5, 9, -14}, {1, 5, 34}, 30]

Formula

G.f.: 1/(1 - 5*x - 9*x^2 + 14*x^3).

a(n) = 5*a(n-1) + 9*a(n-2) - 14*a(n-3) for n >= 3.

a(n) = A359884(n) + 2*a(n-1).