OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Caleb Wagner, Number of tilings of a 4 X n rectangle using integer sided rectangular tiles of area 4, Nov 2013
Index entries for linear recurrences with constant coefficients, signature (1,1,0,5,-1,1,0,-1).
FORMULA
G.f.: -(x-1)*(x+1)*(x^2+1) / (x^8 - x^6 + x^5 - 5*x^4 - x^2 - x + 1).
a(n) = a(n-1) + a(n-2) + 5*a(n-4) - a(n-5) + a(n-6) - a(n-8). - Caleb Wagner, Nov 06 2013
a(2*n+1) = Sum_{k=0..n} A005178(k+1)*a(2*n-2*k). - Shravan Haribalaraman, Aug 29 2022
EXAMPLE
a(3) = 3, because there are 3 tilings of a 4 X 3 rectangle using integer-sided rectangular tiles of area 4:
._._._. ._.___. .___._.
| | | | | | | | | |
| | | | | |___| |___| |
| | | | | | | | | |
|_|_|_| |_|___| |___|_|
MAPLE
gf:= -(x-1)*(x+1)*(x^2+1)/(x^8-x^6+x^5-5*x^4-x^2-x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 05 2012
STATUS
approved