A381475 Array read by antidiagonals: T(m,n) is the connected domination number of the grid graph P_m X P_n.

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 4, 3, 4, 3, 4, 5, 4, 4, 5, 4, 5, 6, 5, 7, 5, 6, 5, 6, 7, 6, 9, 9, 6, 7, 6, 7, 8, 7, 10, 11, 10, 7, 8, 7, 8, 9, 8, 12, 12, 12, 12, 8, 9, 8, 9, 10, 9, 14, 15, 14, 15, 14, 9, 10, 9, 10, 11, 10, 15, 17, 16, 16, 17, 15, 10, 11, 10

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)

Eric Weisstein's World of Mathematics, Connected Domination Number.

Eric Weisstein's World of Mathematics, Grid Graph.

Formula

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

Example

Table begins:
=========================================================
m\n |  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
----+----------------------------------------------------
  1 |  1  1  1  2  3  4  5  6  7  8  9 10 11 12 13 14 ...
  2 |  1  2  2  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
  3 |  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
  4 |  2  4  4  7  9 10 12 14 15 17 19 20 22 24 25 27 ...
  5 |  3  5  5  9 11 12 15 17 18 21 23 24 27 29 30 33 ...
  6 |  4  6  6 10 12 14 16 18 20 22 24 26 28 30 32 34 ...
  7 |  5  7  7 12 15 16 20 23 24 28 31 32 36 39 40 44 ...
  8 |  6  8  8 14 17 18 23 26 27 32 35 36 41 44 45 50 ...
  9 |  7  9  9 15 18 20 24 27 30 33 36 39 42 45 48 51 ...
  ...

Crossrefs

Main diagonal is A369692.

Cf. A300358, A350823, A381474.

Sequence in context: A029215 A240649 A226942 * A030371 A029550 A091110

Adjacent sequences: A381472 A381473 A381474 * A381476 A381477 A381478

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 19 2025

Status

approved