OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Tromino
Index entries for linear recurrences with constant coefficients, signature (1,5,5,1,-1,-1).
FORMULA
G.f.: -(x^3+x^2-1)/(x^6+x^5-x^4-5*x^3-5*x^2-x+1).
a(n) = a(n-1) +5*(a(n-2)+a(n-3)) +a(n-4) -a(n-5) -a(n-6).
EXAMPLE
a(3) = 14:
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_|
|_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_|
.
._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. |
|_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| .
.
MAPLE
a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1, `if`(i=6, [-1$2, 1,
5$2, 1][j], 0)))^n. <<1, 1, 5, 14, 45, 140>>)[1, 1]:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 09 2016
STATUS
approved