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 A127870 #15 Aug 19 2024 08:35:18
%S A127870 1,1,33,195,2023,16839,151817,1328849,11758369,103628653,914646205,
%T A127870 8068452381,71189251649,628067760289,5541284098945,48888866203241,
%U A127870 431331449340441,3805499681885145,33574725778806817,296219181642118401,2613448287490035073
%N A127870 Number of tilings of a 4 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
%H A127870 Alois P. Heinz, <a href="/A127870/b127870.txt">Table of n, a(n) for n = 0..500</a>
%H A127870 P. Chinn, R. Grimaldi and S. Heubach, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Heubach/heubach40.html">Tiling with L's and Squares</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.2.8
%H A127870 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (5, 34, 6, -72, -28, 74, -10, -4, -4).
%F A127870 G.f.: (1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5) / (1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9).
%e A127870 a(2) = 33 because the 4x2 board can be tiled in one way with only square tiles, in 12 ways using one L-tile and 5 square tiles and in 20 ways with 2 L-tiles and 2 square tiles.
%t A127870 Table[Coefficient[Normal[Series[(1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5)/(1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9), {x, 0, 30}]], x, n], {n, 0, 30}]
%Y A127870 Cf. A127864, A127865, A127866, A127867, A127868, A127869.
%Y A127870 Column k=4 of A220054. - _Alois P. Heinz_, Dec 03 2012
%K A127870 nonn
%O A127870 0,3
%A A127870 Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007