A163038 -id:A163038

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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.

+10
12

1, 3, 1, 6, 7, 1, 10, 28, 17, 1, 15, 88, 144, 41, 1, 21, 245, 920, 730, 99, 1, 28, 639, 5191, 9362, 3692, 239, 1, 36, 1608, 27651, 104989, 94280, 18666, 577, 1, 45, 3968, 143342, 1111283, 2075271, 947760, 94384, 1393, 1, 55, 9689, 733512, 11457514, 42972329, 40792921, 9528128, 477264, 3363, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The grid has m rows and n columns.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..435

Chaim Goodman-Strauss, 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 (May 21 2020)

FORMULA

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

EXAMPLE

Array begins: