A291872 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the grid graph P_m X P_n.

1, 3, 3, 4, 9, 4, 4, 24, 24, 4, 4, 56, 129, 56, 4, 4, 136, 613, 613, 136, 4, 4, 328, 2997, 5617, 2997, 328, 4, 4, 792, 14713, 52955, 52955, 14713, 792, 4, 4, 1912, 72169, 502521, 964755, 502521, 72169, 1912, 4, 4, 4616, 353853, 4763717, 17625829, 17625829, 4763717, 353853, 4616, 4

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Grid Graph

Example

Array begins:
===============================================================
m\n| 1   2     3       4         5           6             7
---|-----------------------------------------------------------
1  | 1   3     4       4         4           4             4...
2  | 3   9    24      56       136         328           792...
3  | 4  24   129     613      2997       14713         72169...
4  | 4  56   613    5617     52955      502521       4763717...
5  | 4 136  2997   52955    964755    17625829     321381919...
6  | 4 328 14713  502521  17625829   617429805   21550989109...
7  | 4 792 72169 4763717 321381919 21550989109 1436456861467...
...

Crossrefs

Row 2 is A291706.

Main diagonal is A287690.

Cf. A218354 (dominating), A287151 (connected).

Cf. A291873 (king).

Sequence in context: A049854 A353265 A366758 * A195978 A197280 A197537

Adjacent sequences: A291869 A291870 A291871 * A291873 A291874 A291875

Keyword

nonn,tabl

Author

Andrew Howroyd, Sep 04 2017

Status

approved