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 A278657 #27 Mar 27 2025 11:28:33 %S A278657 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,7,1,1,1,2,25,50,25,2,1,1,3,50, %T A278657 311,311,50,3,1,1,4,155,1954,4101,1954,155,4,1,1,5,508,11914,56864, %U A278657 56864,11914,508,5,1,1,6,1343,76003,728857,1532496,728857,76003,1343,6,1 %N A278657 Number A(n,k) of tilings of a k X n rectangle using pentominoes of any shape and monominoes; square array A(n,k), n>=0, k>=0, read by antidiagonals. %H A278657 Liang Kai, <a href="/A278657/b278657.txt">Antidiagonals n = 0..23, flattened</a> (Antidiagonals n = 0..15 from Alois P. Heinz) %H A278657 Liang Kai, <a href="https://arxiv.org/abs/2503.17698">Solving tiling enumeration problems by tensor network contractions</a>, arXiv:2503.17698 [math.CO], 2025. %H A278657 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a> %e A278657 A(2,3) = A(3,2) = 7: %e A278657 .___. .___. .___. .___. .___. .___. .___. %e A278657 |_|_| | | | | | |_| |_| | | ._| |_. | %e A278657 |_|_| | ._| |_. | | | | | | |_| |_| | %e A278657 |_|_| |_|_| |_|_| |___| |___| |___| |___| . %e A278657 . %e A278657 Square array A(n,k) begins: %e A278657 1, 1, 1, 1, 1, 1, 1, ... %e A278657 1, 1, 1, 1, 1, 2, 3, ... %e A278657 1, 1, 1, 7, 25, 50, 155, ... %e A278657 1, 1, 7, 50, 311, 1954, 11914, ... %e A278657 1, 1, 25, 311, 4101, 56864, 728857, ... %e A278657 1, 2, 50, 1954, 56864, 1532496, 42238426, ... %e A278657 1, 3, 155, 11914, 728857, 42238426, 2492016728, ... %Y A278657 Columns (or rows) k=0-7 give: A000012, A003520, A278874, A278875, A278876, A278456, A278877, A278878. %Y A278657 Cf. A174249, A233427. %K A278657 nonn,tabl %O A278657 0,18 %A A278657 _Alois P. Heinz_, Nov 25 2016