A360918 Array read by antidiagonals: T(m,n) is the number of maximum induced trees in the grid graph P_m X P_n.

1, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 10, 10, 10, 1, 1, 4, 26, 26, 4, 1, 1, 24, 2, 32, 2, 24, 1, 1, 8, 10, 50, 50, 10, 8, 1, 1, 56, 50, 56, 22, 56, 50, 56, 1, 1, 16, 194, 64, 608, 608, 64, 194, 16, 1, 1, 128, 4, 72, 182, 4120, 182, 72, 4, 128, 1, 1, 32, 32, 80, 16, 208, 208, 16, 80, 32, 32, 1

Offset

1,5

Comments

A maximum induced tree is an induced tree of greatest size.

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 ...
---+-------------------------------------------
1  | 1  1   1  1   1     1    1     1     1 ...
2  | 1  4   2 10   4    24    8    56    16 ...
3  | 1  2  10 26   2    10   50   194     4 ...
4  | 1 10  26 32  50    56   64    72    80 ...
5  | 1  4   2 50  22   608  182    16     2 ...
6  | 1 24  10 56 608  4120  208  1968 22716 ...
7  | 1  8  50 64 182   208  488   560  1050 ...
8  | 1 56 194 72  16  1968  560 65864 14340 ...
9  | 1 16   4 80   2 22716 1050 14340   166 ...
   ...

Crossrefs

Main diagonal is A360919.

Cf. A360202, A360847, A360913, A360916, A360920 (maximum sizes).

Sequence in context: A293769 A073693 A360916 * A100261 A370945 A016526

Adjacent sequences: A360915 A360916 A360917 * A360919 A360920 A360921

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 26 2023

Status

approved