A359574 - OEIS

%I #13 Jan 07 2023 14:00:47

%S 1,3,1,6,7,1,10,28,17,1,15,88,144,41,1,21,245,920,730,99,1,28,639,

%T 5191,9362,3692,239,1,36,1608,27651,104989,94280,18666,577,1,45,3968,

%U 143342,1111283,2075271,947760,94384,1393,1,55,9689,733512,11457514,42972329,40792921,9528128,477264,3363,1

%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 bottom row.

%C The grid has m rows and n columns.

%H Andrew Howroyd, <a href="/A359574/b359574.txt">Table of n, a(n) for n = 1..435</a>

%H 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 T(m,n) = A287151(m,n) - 2*A287151(m-1,n) + A287151(m-2,n) for m > 2.

%e Array begins:

%e ================================================================

%e m\n| 1   2     3       4         5           6             7

%e ---+------------------------------------------------------------

%e 1  | 1   3     6      10        15          21            28 ...

%e 2  | 1   7    28      88       245         639          1608 ...

%e 3  | 1  17   144     920      5191       27651        143342 ...

%e 4  | 1  41   730    9362    104989     1111283      11457514 ...

%e 5  | 1  99  3692   94280   2075271    42972329     866126030 ...

%e 6  | 1 239 18666  947760  40792921  1642690309   64270256276 ...

%e 7  | 1 577 94384 9528128 801218515 62618577481 4741764527414 ...

%e   ...

%Y Main diagonal is A163028.

%Y Rows 1..10 are A000217, A163037, A163038, A163039, A163040, A163041, A163042, A163043, A163044, A163045.

%Y Columns 1..10 are A000012, A001333(n+1), A163029, A163030, A163031, A163032, A163033, A163034, A163035, A163036.

%Y Cf. A287151, A292357, A359573, A359576.

%K nonn,tabl

%O 1,2

%A _Andrew Howroyd_, Jan 06 2023