A353878 - OEIS

%I #37 May 14 2022 22:34:38

%S 1,3,44,369,3633,34002,323293,3058623,28982628,274494621,2600148629,

%T 24628666626,233286962601,2209723174731,20930806288252,

%U 198259418947833,1877940242218857,17788105074906162,168491350295593637,1595972975308532199,15117273008425964916

%N Number of tilings of a 3 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.

%C Tiling algorithm see A351322.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,33,3,-40,15).

%F G.f.: (1-3*x-7*x^2+3*x^3-2*x^4) / (1-6*x-33*x^2-3*x^3+40*x^4-15*x^5).

%F a(n) = 6*a(n-1) + 33*a(n-2) + 3*a(n-3) - 40*a(n-4) + 15*a(n-5).

%e a(2)=44

%e The number of tilings (mirroring included) using r trominoes

%e       ___   ___        ___

%e r=1: |  _| | |_| r=2: |  _| r=0: 22 = A030186(3)

%e      |_|3| |___|      |_| |

%e      |___| |_2_|      |___|

%e       4*3 + 4*2   +    2*1   +   22 = 44

%e Legend:

%e    ___              ___      ___

%e   |_2_| stands for |___| or |_|_|

%e      _                _        _        _

%e    _|3|             _| |     _|_|     _|_|

%e   |___| stands for |_|_| or |___| or |_|_|

%o (Maxima) See A352589.

%Y Cf. A030186, A127867, A165716, A351322, A352589, A353877, A353879.

%K nonn,easy

%O 0,2

%A _Gerhard Kirchner_, May 09 2022