A332390 Array read by antidiagonals: T(m,n) is the number of minimal total dominating sets in the m X n king graph.

0, 1, 1, 2, 6, 2, 1, 10, 10, 1, 2, 15, 20, 15, 2, 4, 52, 52, 52, 52, 4, 3, 105, 179, 141, 179, 105, 3, 4, 175, 418, 801, 801, 418, 175, 4, 8, 481, 1167, 2950, 7770, 2950, 1167, 481, 8, 9, 1028, 3498, 9792, 34790, 34790, 9792, 3498, 1028, 9, 10, 2000, 9074, 47527, 184318, 204372, 184318, 47527, 9074, 2000, 10

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..120

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Formula

T(n,m) = T(m,n).

Example

Array begins:
================================================================
m\n | 1   2    3     4       5        6         7          8
----+-----------------------------------------------------------
  1 | 0   1    2     1       2        4         3          4 ...
  2 | 1   6   10    15      52      105       175        481 ...
  3 | 2  10   20    52     179      418      1167       3498 ...
  4 | 1  15   52   141     801     2950      9792      47527 ...
  5 | 2  52  179   801    7770    34790    184318    1305358 ...
  6 | 4 105  418  2950   34790   204372   1593094   14720683 ...
  7 | 3 175 1167  9792  184318  1593094  16260853  231301551 ...
  8 | 4 481 3498 47527 1305358 14720683 231301551 4570906041 ...
  ...

Crossrefs

Rows 1..4 are A302655, A332392, A332393, A332394.

Main diagonal is A332391.

Cf. A286849, A303114, A303118, A303335, A303378.

Sequence in context: A008905 A136760 A303335 * A289382 A062539 A064136

Adjacent sequences: A332387 A332388 A332389 * A332391 A332392 A332393

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 10 2020

Status

approved