

A360196


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


9



1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 5, 14, 24, 14, 5, 6, 20, 58, 58, 20, 6, 7, 27, 125, 229, 125, 27, 7, 8, 35, 251, 749, 749, 251, 35, 8, 9, 44, 490, 2180, 3436, 2180, 490, 44, 9, 10, 54, 948, 6188, 13350, 13350, 6188, 948, 54, 10, 11, 65, 1823, 17912, 50203, 65772, 50203, 17912, 1823, 65, 11
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OFFSET

2,2


COMMENTS

Induced cycles are sometimes called chordless cycles (but some definitions require chordless cycles to have a cycle length of at least 4).


LINKS

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 5 9 14 20 27 35 44 ...
4  3 9 24 58 125 251 490 948 ...
5  4 14 58 229 749 2180 6188 17912 ...
6  5 20 125 749 3436 13350 50203 196918 ...
7  6 27 251 2180 13350 65772 308212 1535427 ...
8  7 35 490 6188 50203 308212 1743247 10614143 ...
9  8 44 948 17912 196918 1535427 10614143 78586742 ...
...


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



