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 A270061 #17 Apr 25 2025 21:02:03 %S A270061 1,1,1,1,1,1,1,1,1,1,1,2,5,2,1,1,3,14,14,3,1,1,4,45,93,45,4,1,1,6,140, %T A270061 590,590,140,6,1,1,9,438,3710,7517,3710,438,9,1,1,13,1371,23509,96176, %U A270061 96176,23509,1371,13,1,1,19,4287,148796,1238818,2501946,1238818,148796,4287,19,1 %N A270061 Number A(n,k) of tilings of a k X n rectangle using monominoes and trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals. %H A270061 Liang Kai, <a href="/A270061/b270061.txt">Antidiagonals n = 0..35, flattened</a> (antidiagonals n = 0..25 from Alois P. Heinz) %H A270061 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tromino">Tromino</a> %e A270061 A(2,3) = A(3,2) = 14: %e A270061 ._____. ._____. ._____. ._____. ._____. ._____. ._____. %e A270061 |_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_| %e A270061 |_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_| %e A270061 . %e A270061 ._____. ._____. ._____. ._____. ._____. ._____. ._____. %e A270061 |_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. | %e A270061 |_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| . %e A270061 . %e A270061 Square array A(n,k) begins: %e A270061 1, 1, 1, 1, 1, 1, 1, ... %e A270061 1, 1, 1, 2, 3, 4, 6, ... %e A270061 1, 1, 5, 14, 45, 140, 438, ... %e A270061 1, 2, 14, 93, 590, 3710, 23509, ... %e A270061 1, 3, 45, 590, 7517, 96176, 1238818, ... %e A270061 1, 4, 140, 3710, 96176, 2501946, 65410388, ... %e A270061 1, 6, 438, 23509, 1238818, 65410388, 3473827027, ... %Y A270061 Columns (or rows) k=0-10 give: A000012, A000930, A270062, A270063, A270064, A270065, A270066, A270067, A270068, A270069, A270070. %Y A270061 Main diagonal gives A270071. %Y A270061 Cf. A233320. %K A270061 nonn,tabl %O A270061 0,12 %A A270061 _Alois P. Heinz_, Mar 09 2016