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%I #6 Dec 17 2025 21:33:59
%S 1,2,1,3,5,1,4,16,12,1,5,44,82,29,1,6,113,469,416,70,1,7,281,2502,
%T 4776,2103,169,1,8,688,12966,50720,48047,10633,408,1,9,1672,66325,
%U 522982,1000725,482895,53767,985,1,10,4049,337222,5323854,20172122,19654292,4854639,271882,2378,1
%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 top row to lower right corner.
%C The grid has m rows and n columns.
%H Andrew Howroyd, <a href="/A391489/b391489.txt">Table of n, a(n) for n = 1..435</a> (first 29 antidiagonals)
%e Array begins:
%e =================================================================
%e m\n| 1 2 3 4 5 6 7 ...
%e ----+------------------------------------------------------------
%e 1 | 1 2 3 4 5 6 7 ...
%e 2 | 1 5 16 44 113 281 688 ...
%e 3 | 1 12 82 469 2502 12966 66325 ...
%e 4 | 1 29 416 4776 50720 522982 5323854 ...
%e 5 | 1 70 2103 48047 1000725 20172122 401252765 ...
%e 6 | 1 169 10633 482895 19654292 769984742 29719343543 ...
%e 7 | 1 408 53767 4854639 385935282 29335294083 2190944084653 ...
%e ...
%Y Main diagonal is A163011.
%Y Columns 1..10 are A000012, A000129(n+1), A163012, A163013, A163014, A163015, A163016, A163017, A163018, A163019.
%Y Rows 1..10 are A000027, A048777(n-1), A163020, A163021, A163022, A163023, A163024, A163025, A163026, A163027.
%Y Cf. A287151, A292357, A359573, A359574, A389687.
%K nonn,tabl
%O 1,2
%A _Andrew Howroyd_, Dec 12 2025