OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,2)
FORMULA
G.f.: -1/(2*x^5+2*x^2-1).
a(n) = 2*(a(n-2)+a(n-5)) for n>4, a(1)=a(3)=0, a(0)=1, a(2)=2, a(4)=4.
EXAMPLE
a(4) = 4:
._______. ._______. ._______. ._______.
|_. |_. | | ._| ._| |_. | ._| | ._|_. |
| | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
| |_| |_| |_| |_| | | |_|_| | |_| | |_|
|___|___| |___|___| |___|___| |___|___|.
a(5) = 2:
._________. ._________.
| | ._____| |_____. | |
| |_| |_. | | ._| |_| |
| |_. ._| | | |_. ._| |
|___|_| | | | | |_|___|
|_______|_| |_|_______|.
MAPLE
a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
<0|0|0|0|1>, <2|0|0|2|0>>^n)[5, 5]:
seq(a(n), n=0..50);
MATHEMATICA
LinearRecurrence[{0, 2, 0, 0, 2}, {1, 0, 2, 0, 4}, 50] (* Jean-François Alcover, May 28 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 23 2013
STATUS
approved