This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353878 #37 May 14 2022 22:34:38 %S A353878 1,3,44,369,3633,34002,323293,3058623,28982628,274494621,2600148629, %T A353878 24628666626,233286962601,2209723174731,20930806288252, %U A353878 198259418947833,1877940242218857,17788105074906162,168491350295593637,1595972975308532199,15117273008425964916 %N A353878 Number of tilings of a 3 X n rectangle using right trominoes, dominoes and 1 X 1 tiles. %C A353878 Tiling algorithm see A351322. %H A353878 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,33,3,-40,15). %F A353878 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 A353878 a(n) = 6*a(n-1) + 33*a(n-2) + 3*a(n-3) - 40*a(n-4) + 15*a(n-5). %e A353878 a(2)=44 %e A353878 The number of tilings (mirroring included) using r trominoes %e A353878 ___ ___ ___ %e A353878 r=1: | _| | |_| r=2: | _| r=0: 22 = A030186(3) %e A353878 |_|3| |___| |_| | %e A353878 |___| |_2_| |___| %e A353878 4*3 + 4*2 + 2*1 + 22 = 44 %e A353878 Legend: %e A353878 ___ ___ ___ %e A353878 |_2_| stands for |___| or |_|_| %e A353878 _ _ _ _ %e A353878 _|3| _| | _|_| _|_| %e A353878 |___| stands for |_|_| or |___| or |_|_| %o A353878 (Maxima) See A352589. %Y A353878 Cf. A030186, A127867, A165716, A351322, A352589, A353877, A353879. %K A353878 nonn,easy %O A353878 0,2 %A A353878 _Gerhard Kirchner_, May 09 2022