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 A127868 #31 Dec 10 2022 08:00:27
%S A127868 3,30,171,1044,5691,30678,159891,821100,4151511,20764590,102880755,
%T A127868 505866804,2471159019,12004723878,58037429739,279405305676,
%U A127868 1340130574407,6406579480446,30536794325547,145166910196116,688444702671291,3257788855054518,15385512460164963
%N A127868 Number of square tiles in all tilings of a 3 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
%H A127868 Robert Israel, <a href="/A127868/b127868.txt">Table of n, a(n) for n = 1..1510</a>
%H A127868 P. Z. Chinn, R. Grimaldi and S. Heubach, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Heubach/heubach40.html">Tiling with Ls and Squares</a>, J. Int. Sequences 10 (2007) #07.2.8.
%H A127868 S. Heubach, <a href="https://www.calstatela.edu/sites/default/files/users/u1231/Presentations/talklv.pdf">Tiling with Ls and Squares</a>, 2005.
%H A127868 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,5,-44,-39,2,-29,4,-4).
%F A127868 G.f.: 3x(1-x)^2(1+6x+3x^2)/(1-3x-7x^2+x^3-2x^4)^2.
%e A127868 a(2) = 30 because the 3 X 2 board can be tiled in one way with only square tiles, in 8 ways using one L-tile and 3 square tiles and in 2 ways with 2 L-tiles, so there are altogether 6 + 8*3 = 30 square tiles in all of the 3x2 tilings.
%p A127868 f:= gfun:-rectoproc({a(n) - 6*a(n-1)-5*a(n-2)+44*a(n-3)+39*a(n-4)-2*a(n-5)+29*a(n-6)-4*a(n-7)+4*a(n-8), a(0) = 0, a(1) = 3, a(2) = 30, a(3) = 171, a(4) = 1044, a(5) = 5691, a(6) = 30678, a(7) = 159891},a(n), remember):
%p A127868 seq(f(n), n=1..40); # _Robert Israel_, Dec 22 2015
%t A127868 Table[Coefficient[Normal[Series[3x(1-x)^2(1+6x+3x^2)/(1-3x-7x^2+x^3-2x^4)^2, {x, 0, 30}]], x, n], {n, 0, 30}]
%t A127868 LinearRecurrence[{6, 5, -44, -39, 2, -29, 4, -4}, {3, 30, 171, 1044, 5691, 30678, 159891, 821100}, 25] (* _Vincenzo Librandi_, Dec 23 2015 *)
%o A127868 (PARI) my(x='x+O('x^100)); Vec(3*x*(1-x)^2*(1+6*x+3*x^2)/(1-3*x-7*x^2+x^3-2*x^4)^2) \\ _Altug Alkan_, Dec 22 2015
%o A127868 (Magma) I:=[3,30,171,1044,5691,30678,159891,821100]; [n le 8 select I[n] else 6*Self(n-1)+5*Self(n-2)-44*Self(n-3)-39*Self(n-4)+2*Self(n-5)-29*Self(n-6)+4*Self(n-7)-4*Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Dec 23 2015
%Y A127868 Cf. A127864, A127865, A127866, A127867, A127869, A127870.
%K A127868 nonn
%O A127868 1,1
%A A127868 Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007