OFFSET
0,4
COMMENTS
a(n) is also the number of ways to tile a 1 X n strip with squares, eight colors of trominoes, and 2 colors of pentominoes.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,8,0,2).
FORMULA
a(n) = a(n-1) + 8*a(n-3) + 2*a(n-5).
G.f.: 1/(1 - x - 8*x^3 - 2*x^5). - Stefano Spezia, Apr 03 2022
EXAMPLE
The a(3) = 9 solutions are as follows:
_____ _____ _____
|_|_|_| | |_| |_| |
|_|_|_| | |_| |_| |
|_|_|_| |_____| |_____|
_____ _____ _____
|_ | | _| | |_|_|
|_| | | |_| | |
|_|___| |___|_| |_____|
_____ _____ _____
|_|_| | | | | |
| | |_ _ | | _ _|
|_____| |_|_|_| |_|_|_|
MATHEMATICA
LinearRecurrence[{1, 0, 8, 0, 2}, {1, 1, 1, 9, 17}, 34];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Drisana Bhatia, Apr 03 2022
STATUS
approved