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A362299
Number of tilings of a 3 X 2n rectangle using dominos and 2 X 2 right triangles.
3
1, 7, 55, 445, 3625, 29575, 241375, 1970125, 16080625, 131254375, 1071334375, 8744528125, 71375265625, 582584734375, 4755218359375, 38813412578125, 316805850390625, 2585857315234375, 21106485396484375, 172276994236328125, 1406172661416015625
OFFSET
0,2
COMMENTS
Triangles only occur as pairs forming 2 X 2 squares. For program code and additional details, see A362297.
FORMULA
a(n) = 10*a(n-1) - 15*a(n-2).
G.f.: (1 - 3*x)/(1 - 10*x + 15*x^2).
E.g.f.: exp(5*x)*(5*cosh(sqrt(10)*x) + sqrt(10)*sinh(sqrt(10)*x))/5. - Stefano Spezia, Apr 20 2023
EXAMPLE
a(1)=7:
___ _ _ ___ ___ _ _ ___ ___ _ _ ___ ___ _
| /| | | | /| |\ | | | |\ | |___| | | |___| | | | |
|/__|_| |_|/__| |__\|_| |_|__\| |___|_| |_|___| |_|_|_|
MATHEMATICA
LinearRecurrence[{10, -15}, {1, 7}, 30] (* Paolo Xausa, Jul 20 2024 *)
CROSSREFS
Row n=3 of A362297.
Sequence in context: A122372 A342935 A083068 * A097189 A049028 A224274
KEYWORD
nonn,easy
AUTHOR
Gerhard Kirchner, Apr 19 2023
STATUS
approved