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
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
KEYWORD
nonn,easy
AUTHOR
Qianyu Guo, Jun 14 2020
EXTENSIONS
More terms from Colin Barker, Jun 14 2020
STATUS
approved