OFFSET
1,7
COMMENTS
Induced cycles are sometimes called chordless cycles (but some definitions require chordless cycles to have a cycle length of at least 4). See A360849 for the version that excludes triangles.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
Eric Weisstein's World of Mathematics, Rook Graph.
Wikipedia, Cycle (graph theory).
EXAMPLE
Array begins:
==========================================================
m\n| 1 2 3 4 5 6 7 8 ...
---+------------------------------------------------------
1 | 0 0 1 4 10 20 35 56 ...
2 | 0 1 5 14 30 55 91 140 ...
3 | 1 5 21 58 125 231 385 596 ...
4 | 4 14 58 236 720 1754 3654 6808 ...
5 | 10 30 125 720 4040 15550 45395 109840 ...
6 | 20 55 231 1754 15550 114105 526505 1776676 ...
7 | 35 91 385 3654 45395 526505 4662721 24865260 ...
8 | 56 140 596 6808 109840 1776676 24865260 256485936 ...
...
PROG
(PARI) T(m, n) = m*binomial(n, 3) + n*binomial(m, 3) + sum(j=2, min(m, n), binomial(m, j)*binomial(n, j)*j!*(j-1)!/2)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 24 2023
STATUS
approved