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A353879 Number of tilings of a 4 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.

%I A353879 #30 Jan 14 2023 12:41:39
%S A353879 1,5,189,3633,83374,1817897,40220893,886130549,19546906987,
%T A353879 431024540644,9505433227293,209617856008535,4622624792880217,
%U A353879 101940750143038657,2248057208102711472,49575464007447758483,1093267021618939507743,24109360928450426884813,531673668551361276666101
%N A353879 Number of tilings of a 4 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.
%C A353879 For tiling algorithm see A351322.
%H A353879 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (14,183,-37,-1929,2419,-212,-333,25,15).
%F A353879 G.f.: (1 - 9*x - 64*x^2 + 109*x^3 + 39*x^4 + 41*x^5 + 12*x^6 - 7*x^7 - 2*x^8) / (1 - 14*x - 183*x^2 + 37*x^3 + 1929*x^4 - 2419*x^5 + 212*x^6 + 333*x^7 - 25*x^8-15*x^9).
%F A353879 a(n) = 14*a(n-1) + 183*a(n-2) - 37*a(n-3) - 1929*a(n-4) + 2419*a(n-5) - 212*a(n-6) - 333*a(n-7) + 25*a(n-8) + 15*a(n-9).
%e A353879 a(2)=189.
%e A353879 The number of tilings (mirroring included) using r trominoes
%e A353879       ___   ___   ___   ___
%e A353879 r=1: |  _| |  _| | |_| |_2_|    r=0: 71 = A030186(4)
%e A353879      |_|_| |_| | |___| |_  |
%e A353879      | 7 | |3|_| | 7 | |3|_|
%e A353879      |___| |___| |___| |___|
%e A353879       4*7 + 4*3 + 4*7 + 4*6 = 92
%e A353879       ___   ___   ___   ___   ___   ___   ___
%e A353879 r=2: |  _| |  _| |  _| |  _| |  _| | |_| | |_|
%e A353879      |_| | |_|2| |_|_| |_|_| |_|_| |___| |___|
%e A353879      |___| | |_| |  _|_|_| | |_  | |_  | |  _|
%e A353879      |_2_| |___| |_|_| |___| |_|_| |_|_| |_|_|
%e A353879       4*2 + 2*2 + 4*1 + 2*1 + 4*1 + 2*1 + 2*1 = 26
%e A353879 Result: a(2) = 71+92+26 = 189.
%e A353879 Legend:
%e A353879    ___              ___      ___
%e A353879   |_2_| stands for |___| or |_|_|
%e A353879      _                _        _        _
%e A353879    _|3|             _| |     _|_|     _|_|
%e A353879   |___| stands for |_|_| or |___| or |_|_|
%e A353879    ___              ___   ___   ___   ___   ___   ___      ___
%e A353879   | 7 |            |___| |_|_| |___| | | | |_| | | |_|    |_|_|
%e A353879   |___| stands for |___|,|___|,|_|_|,|_|_|,|_|_|,|_|_| or |_|_|
%o A353879 (Maxima) See A352589.
%Y A353879 Cf. A030186, A127870, A165791, A351322, A352589, A353877, A353878.
%K A353879 nonn,easy
%O A353879 0,2
%A A353879 _Gerhard Kirchner_, May 09 2022