OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (2,2,5).
FORMULA
G.f.: (x-1)*(x^2+x+1)/(5*x^3+2*x^2+2*x-1).
a(n) = 2*a(n-1)+2*a(n-2)+5*a(n-3) for n>3, a(0)=1; a(1)=2, a(2)=6, a(3)=20.
EXAMPLE
a(2) = 6:
._______. ._______. ._______. ._______. ._______. ._______.
| | | | | | | | | | | | | ._| | | |_. |
| ._| ._| |_. |_. | | ._|_. | |_. | ._| |___| | | |___|
|_| |_| | | |_| |_| |_| | |_| | |_|_| | | |___| |___| |
| | | | | | | | | | | | | ._| | | |_. |
|___|___| |___|___| |___|___| |___|___| |_|_____| |_____|_| .
MAPLE
a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 20][n+1],
2*a(n-1) +2*a(n-2) +5*a(n-3))
end:
seq(a(n), n=0..40);
MATHEMATICA
Join[{1}, LinearRecurrence[{2, 2, 5}, {2, 6, 20}, 40]] (* Jean-François Alcover, May 29 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 17 2014
STATUS
approved