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A362299 Number of tilings of a 3 X 2n rectangle using dominos and 2 X 2 right triangles.

%I A362299 #16 Jul 20 2024 17:18:38
%S A362299 1,7,55,445,3625,29575,241375,1970125,16080625,131254375,1071334375,
%T A362299 8744528125,71375265625,582584734375,4755218359375,38813412578125,
%U A362299 316805850390625,2585857315234375,21106485396484375,172276994236328125,1406172661416015625
%N A362299 Number of tilings of a 3 X 2n rectangle using dominos and 2 X 2 right triangles.
%C A362299 Triangles only occur as pairs forming 2 X 2 squares. For program code and additional details, see A362297.
%H A362299 Paolo Xausa, <a href="/A362299/b362299.txt">Table of n, a(n) for n = 0..1000</a>
%H A362299 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-15).
%F A362299 a(n) = 10*a(n-1) - 15*a(n-2).
%F A362299 G.f.: (1 - 3*x)/(1 - 10*x + 15*x^2).
%F A362299 E.g.f.: exp(5*x)*(5*cosh(sqrt(10)*x) + sqrt(10)*sinh(sqrt(10)*x))/5. - _Stefano Spezia_, Apr 20 2023
%e A362299 a(1)=7:
%e A362299    ___ _    _ ___    ___ _    _ ___    ___ _    _ ___    ___ _
%e A362299   |  /| |  | |  /|  |\  | |  | |\  |  |___| |  | |___|  | | | |
%e A362299   |/__|_|  |_|/__|  |__\|_|  |_|__\|  |___|_|  |_|___|  |_|_|_|
%t A362299 LinearRecurrence[{10, -15}, {1, 7}, 30] (* _Paolo Xausa_, Jul 20 2024 *)
%Y A362299 Row n=3 of A362297.
%Y A362299 Cf. A351322, A352432, A352433, A006130, A362298.
%K A362299 nonn,easy
%O A362299 0,2
%A A362299 _Gerhard Kirchner_, Apr 19 2023