A286847 Array read by antidiagonals: T(m,n) = number of minimal dominating sets in the grid graph P_m X P_n.

1, 2, 2, 2, 6, 2, 4, 7, 7, 4, 4, 18, 16, 18, 4, 7, 39, 53, 53, 39, 7, 9, 75, 154, 306, 154, 75, 9, 13, 155, 436, 1167, 1167, 436, 155, 13, 18, 310, 1268, 4939, 6958, 4939, 1268, 310, 18, 25, 638, 3660, 21313, 40931, 40931, 21313, 3660, 638, 25

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..153

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Example

Table begins:
===============================================================
m\n|  1   2    3     4       5        6         7          8
---|-----------------------------------------------------------
1  |  1   2    2     4       4        7         9         13...
2  |  2   6    7    18      39       75       155        310...
3  |  2   7   16    53     154      436      1268       3660...
4  |  4  18   53   306    1167     4939     21313      88161...
5  |  4  39  154  1167    6958    40931    254754    1519544...
6  |  7  75  436  4939   40931   349178   3118754   26797630...
7  |  9 155 1268 21313  254754  3118754  40307167  497709474...
8  | 13 310 3660 88161 1519544 26797630 497709474 8863408138...
...

Crossrefs

Rows 1-3 are A253412, A290379, A286848.

Main diagonal is A290382.

Cf. A218354 (dominating sets), A089934 (independent), A286868 (irredundant).

Cf. A286849 (king graph).

Sequence in context: A361301 A240501 A278251 * A291439 A023957 A224964

Adjacent sequences: A286844 A286845 A286846 * A286848 A286849 A286850

Keyword

nonn,tabl

Author

Andrew Howroyd, Aug 01 2017

Status

approved