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%I #10 Jan 30 2023 21:05:25
%S 1,1,1,1,3,1,1,8,8,1,1,20,45,20,1,1,49,234,234,49,1,1,119,1193,2423,
%T 1193,119,1,1,288,6049,24455,24455,6049,288,1,1,696,30616,245972,
%U 482443,245972,30616,696,1,1,1681,154861,2473317,9469361,9469361,2473317,154861,1681,1
%N 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 upper left corner to lower right corner.
%H Andrew Howroyd, <a href="/A359573/b359573.txt">Table of n, a(n) for n = 1..435</a>
%F T(m,n) = T(n,m).
%e Array begins:
%e ================================================================
%e m\n| 1 2 3 4 5 6 7
%e ---+------------------------------------------------------------
%e 1 | 1 1 1 1 1 1 1 ...
%e 2 | 1 3 8 20 49 119 288 ...
%e 3 | 1 8 45 234 1193 6049 30616 ...
%e 4 | 1 20 234 2423 24455 245972 2473317 ...
%e 5 | 1 49 1193 24455 482443 9469361 185899132 ...
%e 6 | 1 119 6049 245972 9469361 360923899 13742823032 ...
%e 7 | 1 288 30616 2473317 185899132 13742823032 1012326365581 ...
%e ...
%Y Main diagonal is A163002.
%Y Rows 1..10 are A000012, A048739(n-1), A163003, A163004, A163005, A163006, A163007, A163008, A163009, A163010.
%Y Cf. A287151, A359574, A359575, A359576.
%K nonn,tabl
%O 1,5
%A _Andrew Howroyd_, Jan 06 2023