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 A362297 #23 Apr 29 2023 00:07:54 %S A362297 1,1,1,1,1,1,1,1,4,1,1,1,19,7,1,1,1,97,55,19,1,1,1,508,445,472,40,1,1, %T A362297 1,2683,3625,13249,2023,97,1,1,1,14209,29575,392299,109771,13249,217, %U A362297 1,1,1,75316,241375,11877025,6078148,2102272,66325,508,1,1,1,399331,1970125,362823607,338504101,358815535,22650721,392299,1159,1 %N A362297 Array read by antidiagonals for k,n>=0: T(n,k) = number of tilings of a 2k X n rectangle using dominos and 2 X 2 right triangles. %C A362297 Triangles only occur as pairs forming 2 X 2 squares. Combining four triangles, a square with side sqrt(2) can be made, but this side is irrational and the square cannot be used for tiling. A pair of triangles is equivalent to a 2 X 2 square with a 180 degree rotation symmetry (generated by an ornament for example). %H A362297 Andrew Howroyd, <a href="/A362297/b362297.txt">Table of n, a(n) for n = 0..860</a> (first 41 antidiagonals). %H A362297 Gerhard Kirchner, <a href="/A362297/a362297.pdf">Maxima code</a> %H A362297 Gerhard Kirchner, <a href="/A362297/a362297_1.pdf">Tilings with right triangles</a> %F A362297 T(n,1) = A006130(n). %F A362297 T(n,2) = A362298(n). %F A362297 T(3,k) = A362299(k). %e A362297 Table begins: %e A362297 n\k_0__1_____2_______3_________4___________5______________6 %e A362297 0: 1 1 1 1 1 1 1 %e A362297 1: 1 1 1 1 1 1 1 %e A362297 2: 1 4 19 97 508 2683 14209 %e A362297 3: 1 7 55 445 3625 29575 241375 %e A362297 4: 1 19 472 13249 392299 11877025 362823607 %e A362297 5: 1 40 2023 109771 6078148 338504101 18883136617 %e A362297 6: 1 97 13249 2102272 358815535 63483562159 11428502939791 %Y A362297 Cf. A351322, A352431, A352432, A352433, A006130, A362298, A362299. %K A362297 nonn,tabl %O A362297 0,9 %A A362297 _Gerhard Kirchner_, Apr 19 2023