A360916 Array read by antidiagonals: T(m,n) is the number of maximum induced paths in the grid graph P_m X P_n.

1, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 6, 8, 6, 1, 1, 2, 14, 14, 2, 1, 1, 8, 18, 84, 18, 8, 1, 1, 2, 2, 26, 26, 2, 2, 1, 1, 10, 4, 32, 56, 32, 4, 10, 1, 1, 2, 6, 16, 4, 4, 16, 6, 2, 1, 1, 12, 8, 152, 24, 136, 24, 152, 8, 12, 1, 1, 2, 10, 48, 32, 10, 10, 32, 48, 10, 2, 1

Offset: 1

Author

Andrew Howroyd, Feb 26 2023

Keywords

• nonn
• tabl

Comments

A maximum induced path is an induced path of longest length.

T(m,n) is the number of snake-like polyominoes with the maximum possible number of unit squares in an m X n rectangle.

Examples

			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   6   2   8   2  10   2 ...
3  | 1  2  8  14  18   2   4   6   8 ...
4  | 1  6 14  84  26  32  16 152  48 ...
5  | 1  2 18  26  56   4  24  32 108 ...
6  | 1  8  2  32   4 136  10 168  32 ...
7  | 1  2  4  16  24  10  52   4   8 ...
8  | 1 10  6 152  32 168   4 216   8 ...
9  | 1  2  8  48 108  32   8   8  16 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..435
• Eric Weisstein's World of Mathematics, Grid Graph.

Crossrefs

Main diagonal is A331986.

Cf. A360199, A360913, A360917 (lengths), A360918.

Formula

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