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A352432
Number of tilings of a 4 X n rectangle using dominoes and 2 X 2 tiles.
5
1, 1, 11, 29, 165, 593, 2773, 11093, 48605, 201829, 864901, 3638261, 15472261, 65377669, 277294885, 1173523013, 4972873413, 21056700293, 89200845765, 377774394309, 1600161267781, 6777276186821, 28705824305861, 121582507360709
OFFSET
0,3
COMMENTS
The sequence is based on A352431.
FORMULA
G.f.:(1 - 2*x - 2*x^2 + 4*x^3)/(1 - 3*x - 10*x^2 + 18*x^3 + 14*x^4 - 20*x^5).
a(n) = 3*a(n-1) + 10*a(n-2) - 18*a(n-3) - 14*a(n-4) + 20*a(n-5).
EXAMPLE
a(2)=11:
___ ___ ___ ___ ___ ___
| | | | | | | | | |___| |___|
|___| |___| |___| |_|_| |___| |___|
| | | | | |___| | | | | |___|
|___| |_|_| |___| |___| |___| |___|
.
___ ___ ___ ___ ___
|___| | | | |___| |___| | | |
| | |_|_| | | | |___| |_|_|
|___| | | | |_|_| | | | |___|
|___| |_|_| |___| |_|_| |___|
CROSSREFS
Sequence in context: A080083 A115972 A099109 * A302091 A122095 A282137
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Mar 17 2022
STATUS
approved