A335559 a(n) = 3*a(n-1) + 4*a(n-2) - 2*a(n-3) with a(0)=0, a(1)=1, a(2)=2.

0, 1, 2, 10, 36, 144, 556, 2172, 8452, 32932, 128260, 499604, 1945988, 7579860, 29524324, 115000436, 447938884, 1744769748, 6796063908, 26471392948, 103108894980, 401620128916, 1564353180772, 6093322268020, 23734139269316, 92447000518484, 360090914096676

Offset

0,3

Comments

For n > 0, a(n) is the number of ways to tile a 2 X 2 X (n-1) box with 1 X 1 X 1 cubes and 1 X 2 X 2 plates.

Links

Table of n, a(n) for n=0..26.

Qianyu Guo, Cube-plate Tiling Numbers and Their Identities, Pioneer Academics, Vol 7, pp. 227-237, 2020.

Index entries for linear recurrences with constant coefficients, signature (3,4,-2).

Formula

G.f.: (1 - x) / (1 - 3*x - 4*x^2 + 2*x^3). - Colin Barker, Jun 14 2020

Example

Here are four of the a(4) = 36 possible tilings of a 2 x 2 x 3 box with cubes and plates:
. ______     ______     ______     _______
./ / / /|   / /___/|   /___/ /|   / /    /|
/_/_/_/ |  /_/___/||  /___/_/ |  /_/___ //|
| | | | /  | |   ||/  |   | | /  | |___|//
|_|_|_|/   |_|___|/   |_ _|_|/   |_|___|/

Mathematica

LinearRecurrence[{3, 4, -2}, {0, 1, 2}, 30] (* Greg Dresden, Jun 14 2020 *)

Prog

(PARI) Vec((1 - x) / (1 - 3*x - 4*x^2 + 2*x^3) + O(x^30)) \\ Colin Barker, Jun 14 2020

Crossrefs

Cf. A006253, A237358, A237355, A237356.

Sequence in context: A265844 A192858 A202796 * A001582 A357035 A370713

Adjacent sequences: A335556 A335557 A335558 * A335560 A335561 A335562

Keyword

nonn,easy

Author

Qianyu Guo, Jun 14 2020

Extensions

More terms from Colin Barker, Jun 14 2020

Status

approved