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A287151 Array read by antidiagonals: T(m,n) = number of nonzero m X n binary arrays with all 1's connected. 7
1, 3, 3, 6, 13, 6, 10, 40, 40, 10, 15, 108, 218, 108, 15, 21, 275, 1126, 1126, 275, 21, 28, 681, 5726, 11506, 5726, 681, 28, 36, 1664, 28992, 116166, 116166, 28992, 1664, 36, 45, 4040, 146642, 1168586, 2301877, 1168586, 146642, 4040, 45 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the number of connected induced (non-null) subgraphs of the grid graph P_m X P_n.

LINKS

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

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Induced Subgraph

EXAMPLE

Table starts:

====================================================================

m\n|  1    2      3        4         5           6             7

---|----------------------------------------------------------------

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

2  |  3   13     40      108       275         681          1664 ...

3  |  6   40    218     1126      5726       28992        146642 ...

4  | 10  108   1126    11506    116166     1168586      11749134 ...

5  | 15  275   5726   116166   2301877    45280509     889477656 ...

6  | 21  681  28992  1168586  45280509  1732082741   66037462454 ...

7  | 28 1664 146642 11749134 889477656 66037462454 4872949974666 ...

...

CROSSREFS

Rows 2-4 are A059020, A059021, A059524.

Main diagonal is A059525.

Cf. A116469, A286139, A286189.

Sequence in context: A168076 A168073 A231829 * A123140 A123289 A096572

Adjacent sequences:  A287148 A287149 A287150 * A287152 A287153 A287154

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, May 20 2017

STATUS

approved

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Last modified August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)