A360913 Array read by antidiagonals: T(m,n) is the number of maximum induced cycles in the grid graph P_m X P_n.

1, 2, 2, 3, 1, 3, 4, 1, 1, 4, 5, 1, 7, 1, 5, 6, 1, 17, 17, 1, 6, 7, 1, 31, 90, 31, 1, 7, 8, 1, 8, 284, 284, 8, 1, 8, 9, 1, 40, 9, 1398, 9, 40, 1, 9, 10, 1, 120, 163, 10, 10, 163, 120, 1, 10, 11, 1, 8, 1329, 382, 23, 382, 1329, 8, 1, 11, 12, 1, 64, 128, 6098, 190, 190, 6098, 128, 64, 1, 12

Offset

2,2

Comments

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

Links

Table of n, a(n) for n=2..79.

Eric Weisstein's World of Mathematics, Grid Graph.

Formula

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

Example

Array begins:
=========================================
m\n| 2  3   4    5    6   7    8    9 ...
---+-------------------------------------
2  | 1  2   3    4    5   6    7    8 ...
3  | 2  1   1    1    1   1    1    1 ...
4  | 3  1   7   17   31   8   40  120 ...
5  | 4  1  17   90  284   9  163 1329 ...
6  | 5  1  31  284 1398  10  382 6098 ...
7  | 6  1   8    9   10  23  190  388 ...
8  | 7  1  40  163  382 190 2100   80 ...
9  | 8  1 120 1329 6098 388   80 6840 ...
  ...

Crossrefs

Main diagonal is A360914.

Cf. A360196 (induced cycles), A360915 (lengths), A360916, A360918.

Sequence in context: A245327 A352680 A131821 * A204123 A237448 A204143

Adjacent sequences: A360910 A360911 A360912 * A360914 A360915 A360916

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 26 2023

Status

approved