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 A359574 #13 Jan 07 2023 14:00:47 %S A359574 1,3,1,6,7,1,10,28,17,1,15,88,144,41,1,21,245,920,730,99,1,28,639, %T A359574 5191,9362,3692,239,1,36,1608,27651,104989,94280,18666,577,1,45,3968, %U A359574 143342,1111283,2075271,947760,94384,1393,1,55,9689,733512,11457514,42972329,40792921,9528128,477264,3363,1 %N A359574 Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and a path of 1's from top row to bottom row. %C A359574 The grid has m rows and n columns. %H A359574 Andrew Howroyd, <a href="/A359574/b359574.txt">Table of n, a(n) for n = 1..435</a> %H A359574 Chaim Goodman-Strauss, <a href="/A163029/a163029.pdf">Notes on the number of m × n binary arrays with all 1's connected and a path of 1's from top row to bottom row</a> (May 21 2020) %F A359574 T(m,n) = A287151(m,n) - 2*A287151(m-1,n) + A287151(m-2,n) for m > 2. %e A359574 Array begins: %e A359574 ================================================================ %e A359574 m\n| 1 2 3 4 5 6 7 %e A359574 ---+------------------------------------------------------------ %e A359574 1 | 1 3 6 10 15 21 28 ... %e A359574 2 | 1 7 28 88 245 639 1608 ... %e A359574 3 | 1 17 144 920 5191 27651 143342 ... %e A359574 4 | 1 41 730 9362 104989 1111283 11457514 ... %e A359574 5 | 1 99 3692 94280 2075271 42972329 866126030 ... %e A359574 6 | 1 239 18666 947760 40792921 1642690309 64270256276 ... %e A359574 7 | 1 577 94384 9528128 801218515 62618577481 4741764527414 ... %e A359574 ... %Y A359574 Main diagonal is A163028. %Y A359574 Rows 1..10 are A000217, A163037, A163038, A163039, A163040, A163041, A163042, A163043, A163044, A163045. %Y A359574 Columns 1..10 are A000012, A001333(n+1), A163029, A163030, A163031, A163032, A163033, A163034, A163035, A163036. %Y A359574 Cf. A287151, A292357, A359573, A359576. %K A359574 nonn,tabl %O A359574 1,2 %A A359574 _Andrew Howroyd_, Jan 06 2023