A360918 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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