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 A361523 #10 Mar 20 2023 13:08:56 %S A361523 1,1,1,1,2,4,1,3,17,54,1,6,61,892,9235,1,10,220,8159,406653,10538496 %N A361523 Triangle read by rows: T(n,k) is the number of ways of dividing an n X k rectangle into integer-sided rectangles, up to rotations and reflections. %F A361523 T(n,k) >= A116694(n,k)/4 if n != k. %F A361523 T(n,n) >= A116694(n,n)/8. %e A361523 Triangle begins: %e A361523 n\k| 0 1 2 3 4 5 %e A361523 ---+------------------------------ %e A361523 0 | 1 %e A361523 1 | 1 1 %e A361523 2 | 1 2 4 %e A361523 3 | 1 3 17 54 %e A361523 4 | 1 6 61 892 9235 %e A361523 5 | 1 10 220 8159 406653 10538496 %e A361523 The 3 X 2 rectangle can be divided in T(3,2) = 17 inequivalent ways: %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | | | %e A361523 + + +---+---+ +---+---+ + + + + +---+ + +---+ %e A361523 | | | | | | | | | | | | | | | %e A361523 + + + + + + + + + + + + + +---+ %e A361523 | | | | | | | | | | | | | | | %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 . %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | | | %e A361523 +---+---+ + + + +---+---+ + +---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | | | %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ + + + %e A361523 | | | | | | | | | | | | | %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 . %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | | %e A361523 +---+ + +---+---+ +---+---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | %e A361523 + +---+ +---+---+ + +---+ +---+---+ +---+---+ %e A361523 | | | | | | | | | | | | | | %e A361523 +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ %Y A361523 Main diagonal: A361524. %Y A361523 Columns: A000012 (k = 0), A005418 (k = 1), A347825 (k = 2; with an exception for n = 2), A361525 (k = 3), A361526 (k = 4). %Y A361523 Cf. A116694 (rotations and reflections are considered distinct), A227690 (square pieces), A360629. %K A361523 nonn,tabl,more %O A361523 0,5 %A A361523 _Pontus von Brömssen_, Mar 15 2023