A303114 Array read by antidiagonals: T(m,n) = number of total dominating sets in the n X m king graph.

0, 1, 1, 3, 11, 3, 4, 47, 47, 4, 5, 165, 353, 165, 5, 9, 625, 2545, 2545, 625, 9, 16, 2435, 19651, 35458, 19651, 2435, 16, 25, 9367, 150719, 538977, 538977, 150719, 9367, 25, 39, 35901, 1149593, 8213971, 16322279, 8213971, 1149593, 35901, 39

Offset

1,4

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Example

Table begins:
============================================================================
m\n|  1    2       3         4           5             6               7
---|------------------------------------------------------------------------
1  |  0    1       3         4           5             9              16 ...
2  |  1   11      47       165         625          2435            9367 ...
3  |  3   47     353      2545       19651        150719         1149593 ...
4  |  4  165    2545     35458      538977       8213971       124153394 ...
5  |  5  625   19651    538977    16322279     496873689     14980146565 ...
6  |  9 2435  150719   8213971   496873689   30158547693   1812834702647 ...
7  | 16 9367 1149593 124153394 14980146565 1812834702647 217221533288240 ...
...

Crossrefs

Rows 1..2 are A195971(n-1), A219079.

Main diagonal is A303116.

Cf. A218663 (dominating sets), A291873 (connected dominating sets).

Cf. A303111 (grid graph).

Sequence in context: A110221 A244237 A238683 * A359990 A170856 A176781

Adjacent sequences: A303111 A303112 A303113 * A303115 A303116 A303117

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 18 2018

Status

approved