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Andrew Howroyd, <a href="/A360916/b360916.txt">Table of n, a(n) for n = 1..435</a>

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

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

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

allocated for Andrew HowroydArray 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

1,5

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

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.

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 ...

...

Main diagonal is A331986.

Cf. A360199, A360913, A360917 (lengths).

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nonn,tabl

Andrew Howroyd, Feb 26 2023

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allocated for Andrew Howroyd

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