A360920 Array read by antidiagonals: T(m,n) is the maximum number of vertices in an induced tree in the grid graph P_m X P_n.

1, 2, 2, 3, 3, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 6, 8, 9, 9, 8, 6, 7, 9, 12, 12, 12, 9, 7, 8, 11, 14, 15, 15, 14, 11, 8, 9, 12, 16, 18, 19, 18, 16, 12, 9, 10, 14, 18, 21, 22, 22, 21, 18, 14, 10, 11, 15, 21, 24, 26, 26, 26, 24, 21, 15, 11, 12, 17, 23, 27, 30, 31, 31, 30, 27, 23, 17, 12

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Grid Graph.

Formula

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

Example

Array begins:
===============================================
  m\n|  1  2  3  4  5  6  7  8  9 10 11  12 ...
-----+-----------------------------------------
   1 |  1  2  3  4  5  6  7  8  9 10 11  12 ...
   2 |  2  3  5  6  8  9 11 12 14 15 17  18 ...
   3 |  3  5  7  9 12 14 16 18 21 23 25  27 ...
   4 |  4  6  9 12 15 18 21 24 27 30 33  36 ...
   5 |  5  8 12 15 19 22 26 30 34 37 41  44 ...
   6 |  6  9 14 18 22 26 31 35 39 44 48  52 ...
   7 |  7 11 16 21 26 31 36 41 46 51 56  61 ...
   8 |  8 12 18 24 30 35 41 46 52 58 63  69 ...
   9 |  9 14 21 27 34 39 46 52 59 65 71  78 ...
  10 | 10 15 23 30 37 44 51 58 65 72 79  86 ...
  11 | 11 17 25 33 41 48 56 63 71 79 87  94 ...
  12 | 12 18 27 36 44 52 61 69 78 86 94 102 ...
  ...

Crossrefs

Main diagonal is A360921.

Cf. A360915, A360917, A360918 (maximum induced trees).

Sequence in context: A350066 A360917 A135646 * A334922 A301851 A101646

Adjacent sequences: A360917 A360918 A360919 * A360921 A360922 A360923

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 26 2023

Status

approved