OFFSET
0,2
COMMENTS
a(n) is the number of ways to tile a 3 X (2*n) rectangle with two kinds of tiles: dominoes (made up of 2 cells) and T's (made up of 4 cells), each of which can be rotated as needed.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,7,4,-8,2).
FORMULA
a(n) = 5*a(n-1) + 7*a(n-2) + 4*a(n-3) - 8*a(n-4) + 2*a(n-5).
G.f.: -(2*x^4-3*x^3-4*x^2-2*x+1)/(2*x^5-8*x^4+4*x^3+7*x^2+5*x-1).
EXAMPLE
For n=3, here is one of the a(3) = 112 ways to tile a 3 x 6 rectangle using our dominoes and T's:
___________
| |___| | | |
| _|_ |_|_|
|_|___|_|___|.
MATHEMATICA
LinearRecurrence[{5, 7, 4, -8, 2}, {1, 3, 18, 112, 692}, 30] (* Paolo Xausa, Sep 23 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Lucas MingQu Xia, Sep 06 2024
STATUS
approved