OFFSET
0,5
COMMENTS
The absolute value of a(n) is the number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, X. |a(3)| = 1, |a(4)| = 2:
._____. ._______. ._______.
| ._. | | ._. | | | | ._. |
|_| |_| |_| |_| | | |_| |_|
|_. ._| , | ._| ._| |_. |_. |
| |_| | | | |_| | | |_| | |
|_____| |_|_____| |_____|_|. - Alois P. Heinz, Jan 03 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0,0,-1,2)
FORMULA
a(n) = (-1)^n*sum(A128099(n-2*k, n-3*k), k=0..floor(n/3)). - Johannes W. Meijer, Aug 28 2013
G.f.: 1/(1 + x^3 - 2*x^4). - Arkadiusz Wesolowski, Nov 20 2013
MAPLE
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|-1|0|0>>^n.
<<1, 0, 0, -1>>)[1, 1]:
seq(a(n), n=0..60); # Alois P. Heinz, Nov 20 2013
MATHEMATICA
CoefficientList[1/(1+x^3-2*x^4) + O[x]^60, x] (* Jean-François Alcover, Jun 08 2015, after Arkadiusz Wesolowski *)
PROG
(PARI) Vec( 1/((1-x)*(1+x+x^2+2*x^3)) +O(x^66)) \\ Joerg Arndt, Aug 28 2013
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved