login
A220123
Number of tilings of a 4 X n rectangle using integer-sided rectangular tiles of area 4.
2
1, 1, 2, 3, 9, 16, 35, 65, 143, 281, 590, 1174, 2440, 4925, 10142, 20563, 42178, 85819, 175632, 357875, 731536, 1491966, 3047879, 6218844, 12699982, 25919176, 52922491, 108022099, 220541999, 450186874, 919074255, 1876149465, 3830134125, 7818778884, 15961716918
OFFSET
0,3
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
Column k=4 of A220122. Cf. A005178.
Sequence in context: A173809 A298355 A023147 * A220125 A095742 A011951
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 05 2012
STATUS
approved