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A219925
Number of tilings of a 6 X n rectangle using integer-sided square tiles.
11
1, 1, 13, 60, 348, 1916, 10668, 59257, 329350, 1830234, 10171315, 56525022, 314128014, 1745708992, 9701463927, 53914132251, 299618062228, 1665073290365, 9253344266757, 51423790446062, 285778433090830, 1588162056821687, 8825923956549044, 49048479247236561
OFFSET
0,3
LINKS
FORMULA
G.f.: see Maple program.
EXAMPLE
a(2) = 13, because there are 13 tilings of a 6 X 2 rectangle using integer-sided square tiles:
._._. .___. ._._. ._._. ._._. ._._.
|_|_| | | |_|_| |_|_| |_|_| |_|_|
|_|_| |___| | | |_|_| |_|_| |_|_|
|_|_| |_|_| |___| | | |_|_| |_|_|
|_|_| |_|_| |_|_| |___| | | |_|_|
|_|_| |_|_| |_|_| |_|_| |___| | |
|_|_| |_|_| |_|_| |_|_| |_|_| |___|
.___. .___. .___. ._._. ._._. ._._. .___.
| | | | | | |_|_| |_|_| |_|_| | |
|___| |___| |___| | | | | |_|_| |___|
| | |_|_| |_|_| |___| |___| | | | |
|___| | | |_|_| | | |_|_| |___| |___|
|_|_| |___| | | |___| | | | | | |
|_|_| |_|_| |___| |_|_| |___| |___| |___|
MAPLE
gf:= -(2*x^9 +3*x^8 +2*x^7 -3*x^6 -7*x^5 -4*x^4 -3*x^3 +5*x^2 +2*x -1) / (2*x^15 +7*x^14 +12*x^13 +6*x^12 -18*x^11 -13*x^10 -8*x^9 -27*x^8 -32*x^7 +x^6 +40*x^5 +34*x^4 -3*x^3 -15*x^2 -3*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq (a(n), n=0..40);
CROSSREFS
Column k=6 of A219924.
Cf. A226549.
Sequence in context: A354670 A220711 A295915 * A228282 A303806 A304853
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 01 2012
STATUS
approved