OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1, 1, 11, -9, -8, -48, 29, 23, 115, -44, -31, -173, 35, 19, 174, -18, 2, -119, 10, -14, 56, -8, 12, -19, 4, -5, 5, -1, 1, -1).
FORMULA
G.f.: see Maple program.
EXAMPLE
a(3) = 3, because there are 3 tilings of a 4 X 3 rectangle using straight (3 X 1) trominoes and 2 X 2 tiles:
._____. ._____. ._._._.
| | | | |_____| |_____|
| | | | | | | | |_____|
|_|_|_| | | | | |_____|
|_____| |_|_|_| |_____|
a(4) = 3, because there are 3 tilings of a 4 X 4 rectangle using straight (3 X 1) trominoes and 2 X 2 tiles:
._._____. ._____._. ._._._._.
| |_____| |_____| | | . | . |
| | . | | | | . | | |___|___|
|_|___| | | |___|_| | . | . |
|_____|_| |_|_____| |___|___|
MAPLE
gf:= -(x^3+x-1) *(x^18 -3*x^15 +x^14 +7*x^12 -3*x^11 -11*x^9 +3*x^8 +12*x^6 -x^5 -6*x^3+1) *(x-1)^2 *(x^2+x+1)^2 / (x^30 -x^29 +x^28 -5*x^27 +5*x^26 -4*x^25 +19*x^24 -12*x^23 +8*x^22 -56*x^21 +14*x^20 -10*x^19 +119*x^18 -2*x^17 +18*x^16 -174*x^15 -19*x^14 -35*x^13 +173*x^12 +31*x^11 +44*x^10 -115*x^9 -23*x^8 -29*x^7 +48*x^6 +8*x^5 +9*x^4 -11*x^3 -x^2 -x+1):
a:= n-> coeff(series(gf, x, n+1), x, n);
seq(a(n), n=0..50);
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Alois P. Heinz, Dec 20 2011
STATUS
approved