A287151 Array read by antidiagonals: T(m,n) = number of nonzero m X n binary arrays with all 1's connected.

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

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