OFFSET
0,3
COMMENTS
The shapes of the tiles are:
._.
._. | |
._. | |_. | |_._.
|_| |___| |_____| .
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Polyomino
Index entries for linear recurrences with constant coefficients, signature (1,2,3,1).
FORMULA
G.f.: -1/((x^2+x+1)*(x^2+2*x-1)).
a(n) = 2*a(n-1) + a(n-2) + A049347(n). - Greg Dresden, May 18 2020
EXAMPLE
a(3) = 8:
._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____.
|_|_|_| | |_|_| |_|_|_| |_| |_| |_|_|_| |_| |_| | |_|_| | | |_|
|_|_|_| |___|_| | |_|_| |_|___| |_| |_| | |___| | |_|_| | |___|
|_|_|_| |_|_|_| |___|_| |_|_|_| |_|___| |___|_| |_____| |_____| .
MAPLE
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|3|2|1>>^n)[4$2]:
seq(a(n), n=0..40);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 12 2018
STATUS
approved