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 A351322 #34 Apr 20 2023 14:55:20 %S A351322 1,1,1,1,0,1,1,0,2,1,1,0,4,0,1,1,0,8,8,4,1,1,0,16,0,18,0,1,1,0,32,64, %T A351322 88,72,8,1,1,0,64,0,468,384,162,0,1,1,0,128,512,2672,8544,4312,520,16, %U A351322 1,1,0,256,0,16072,76800,118586,22656,1514,0,1,1,0,512,4096,100064,1168512,3403624,1795360,204184,4312,32,1 %N A351322 Number T(n,k) of tilings of a 3k X n rectangle with right trominoes. %C A351322 The table is read by descending antidiagonals. %C A351322 If read by columns or rows: %C A351322 T(n,1) = A077957(n+1) %C A351322 T(2,k) = A000079(k) = 2^k %C A351322 T(4,k) = A046984(k) %C A351322 T(5,k) = A084478(k) %C A351322 T(n,2) = A351323(n) %C A351322 T(7,k) = A351324(k) %C A351322 Linear recurrences with different numbers of parameters are known for the sequences above. %C A351322 Overview: %C A351322 Constant Number of %C A351322 side length Sequence parameters %C A351322 2 T(2,k) 1 %C A351322 3 T(n,1),T(3,k) 2 %C A351322 4 T(4,k) 3 see A046984 %C A351322 5 T(5,k) 4 see A084478 %C A351322 6 T(n,2),T(6,k) 11 see A351323 %C A351322 7 T(7,k) 17 see A351324 %C A351322 8 T(8,k) >30 %C A351322 9 T(n,3),T(9,k) >30 %H A351322 Andrew Howroyd, <a href="/A351322/b351322.txt">Table of n, a(n) for n = 0..495</a> (first 31 antidiagonals). %H A351322 Gerhard Kirchner, <a href="/A351322/a351322_2.pdf">Tiling algorithm</a> %H A351322 Gerhard Kirchner, <a href="/A351322/a351322.txt">Maxima Code</a> %H A351322 Gerhard Kirchner, <a href="/A351322/a351322_1.txt">More sequences</a> %H A351322 Cristopher Moore, <a href="https://arxiv.org/abs/math/9905012">Some Polyomino Tilings of the Plane</a>, arXiv:math/9905012 [math.CO], 1999. %e A351322 6 X 2 rectangle: 4 tilings %e A351322 ___ ___ ___ ___ %e A351322 | _| | _| |_ | |_ | %e A351322 |_| | |_| | | |_| | |_| %e A351322 |___| |___| |___| |___| %e A351322 | _| |_ | | _| |_ | %e A351322 |_| | | |_| |_| | | |_| %e A351322 |___| |___| |___| |___| %e A351322 . %e A351322 Table T(n,k) begins: %e A351322 n\k__0__1______2_________3_____________4 %e A351322 0: 1 1 1 1 1 %e A351322 1: 1 0 0 0 0 %e A351322 2: 1 2 4 8 16 %e A351322 3: 1 0 8 0 64 %e A351322 4: 1 4 18 88 468 %e A351322 5: 1 0 72 384 8544 %e A351322 6: 1 8 162 4312 118586 %e A351322 7: 1 0 520 22656 1795360 %e A351322 8: 1 16 1514 204184 29986082 %e A351322 9: 1 0 4312 1193600 467966840 %e A351322 10: 1 32 13242 9567192 7758809670 %e A351322 11: 1 0 39088 63112256 124693887784 %o A351322 (Maxima) See Maxima Code link. %Y A351322 Cf. A077957, A000079, A046984, A084478, A351323, A351324. %K A351322 nonn,tabl %O A351322 0,9 %A A351322 _Gerhard Kirchner_, Feb 21 2022