OFFSET
0,5
LINKS
Paul Tek, Table of n, a(n) for n = 0..1000
Paul Tek, Illustration of the formula
Paul Tek, Illustration of the first terms
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1).
FORMULA
[ 0 1 0 1 0 0 0 ] [1]
[ 0 0 1 0 0 0 0 ] [0]
[ 0 0 1 1 0 0 0 ] [1]
a(n) = [1 0 0 0 0 0 0] * [ 0 0 0 0 1 0 0 ] ^ n * [0], for any n>=0.
[ 0 0 0 0 0 1 0 ] [0]
[ 0 0 0 0 0 0 1 ] [0]
[ 0 1 0 0 0 1 0 ] [1]
G.f.: -(x^2-x+1)*(x^4-x^2+1) / (x^6-x^3+x^2+x-1). - Colin Barker, Mar 05 2015
EXAMPLE
A 3 X 1 rectangle can be tiled in three ways:
+-+-+-+ +-+---+ +---+-+
| | | |, | | | and | | |.
+-+-+-+ +-+---+ +---+-+
The first tiling is acceptable, as every 1 X 1 tile is next to another 1 X 1 tile (and there are no 2 X 1 tiles).
The second and third tilings are not acceptable, as the 1 X 1 tiles are not next to other 1 X 1 tiles.
Hence, a(3)=1.
PROG
(PARI) Vec(-(x^2-x+1)*(x^4-x^2+1)/(x^6-x^3+x^2+x-1) + O(x^100)) \\ Colin Barker, Mar 05 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Tek, Mar 05 2015
STATUS
approved