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A337492 a(n) = a(n-1) + 4*a(n-3) + 2*a(n-4) + 2*a(n-5); a(0) = a(1) = a(2) = 1, a(3) = 5, a(4) = 11.

%I A337492 #17 Dec 08 2021 11:15:50
%S A337492 1,1,1,5,11,19,43,99,207,439,959,2071,4439,9567,20647,44463,95751,
%T A337492 206351,444631,957855,2063687,4446415,9579799,20639519,44468263,
%U A337492 95807663,206418167,444729855,958176071
%N A337492 a(n) = a(n-1) + 4*a(n-3) + 2*a(n-4) + 2*a(n-5); a(0) = a(1) = a(2) = 1, a(3) = 5, a(4) = 11.
%C A337492 Number of tilings of a 3 X n rectangle with 1 X 1 squares and L-shaped tiles (where the L-shaped tile covers 5 squares).
%H A337492 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,4,2,2).
%F A337492 G.f.: 1/(1-x-4*x^3-2*x^4-2*x^5). - _R. J. Mathar_, Sep 03 2020
%F A337492 Sum_{k=0..n} a(k) = (a(n+3)+4*a(n)+2*a(n-1)-1)/8. - _Sujay Champati_, Sep 05 2020
%e A337492 Here is one of the 11 ways to tile a 3 X 4 rectangle:
%e A337492 ._______
%e A337492 | |_|_|_|
%e A337492 | |_|_|_|
%e A337492 |_ _ _|_|
%t A337492 LinearRecurrence[{1, 0, 4, 2, 2}, {1, 1, 1, 5, 11}, 50]
%Y A337492 Cf. A127864, A127867.
%K A337492 nonn,easy
%O A337492 0,4
%A A337492 _Sujay Champati_ and _Greg Dresden_, Aug 29 2020