cp's OEIS Frontend

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.

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.

This page as a plain text file.
%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