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A360855
Array read by antidiagonals: T(m,n) is the number of triangles in the rook graph K_m X K_n.
4
0, 0, 0, 1, 0, 1, 4, 2, 2, 4, 10, 8, 6, 8, 10, 20, 20, 16, 16, 20, 20, 35, 40, 35, 32, 35, 40, 35, 56, 70, 66, 60, 60, 66, 70, 56, 84, 112, 112, 104, 100, 104, 112, 112, 84, 120, 168, 176, 168, 160, 160, 168, 176, 168, 120, 165, 240, 261, 256, 245, 240, 245, 256, 261, 240, 165
OFFSET
1,7
COMMENTS
A triangle is a clique of size 3. Also, a 3-cycle.
LINKS
Eric Weisstein's World of Mathematics, Rook Graph.
FORMULA
T(m,n) = m*binomial(n,3) + n*binomial(m,3).
T(m,n) = T(n,m).
EXAMPLE
Array begins:
=======================================
m\n| 1 2 3 4 5 6 7 8 ...
---+-----------------------------------
1 | 0 0 1 4 10 20 35 56 ...
2 | 0 0 2 8 20 40 70 112 ...
3 | 1 2 6 16 35 66 112 176 ...
4 | 4 8 16 32 60 104 168 256 ...
5 | 10 20 35 60 100 160 245 360 ...
6 | 20 40 66 104 160 240 350 496 ...
7 | 35 70 112 168 245 350 490 672 ...
8 | 56 112 176 256 360 496 672 896 ...
...
PROG
(PARI) T(m, n) = m*binomial(n, 3) + n*binomial(m, 3)
CROSSREFS
Main diagonal is A288961.
Rows n=1..3 are A000292(n-2), A007290, A060354.
Sequence in context: A021707 A126560 A289762 * A064213 A354102 A245518
KEYWORD
nonn,tabl,easy
AUTHOR
Andrew Howroyd, Feb 24 2023
STATUS
approved