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A353878
Number of tilings of a 3 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.
3
1, 3, 44, 369, 3633, 34002, 323293, 3058623, 28982628, 274494621, 2600148629, 24628666626, 233286962601, 2209723174731, 20930806288252, 198259418947833, 1877940242218857, 17788105074906162, 168491350295593637, 1595972975308532199, 15117273008425964916
OFFSET
0,2
COMMENTS
Tiling algorithm see A351322.
FORMULA
G.f.: (1-3*x-7*x^2+3*x^3-2*x^4) / (1-6*x-33*x^2-3*x^3+40*x^4-15*x^5).
a(n) = 6*a(n-1) + 33*a(n-2) + 3*a(n-3) - 40*a(n-4) + 15*a(n-5).
EXAMPLE
a(2)=44
The number of tilings (mirroring included) using r trominoes
___ ___ ___
r=1: | _| | |_| r=2: | _| r=0: 22 = A030186(3)
|_|3| |___| |_| |
|___| |_2_| |___|
4*3 + 4*2 + 2*1 + 22 = 44
Legend:
___ ___ ___
|_2_| stands for |___| or |_|_|
_ _ _ _
_|3| _| | _|_| _|_|
|___| stands for |_|_| or |___| or |_|_|
PROG
(Maxima) See A352589.
KEYWORD
nonn,easy
AUTHOR
Gerhard Kirchner, May 09 2022
STATUS
approved