OFFSET
1,4
COMMENTS
Paths of length zero are not counted here.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
Eric Weisstein's World of Mathematics, Rook Graph.
Wikipedia, Induced path.
FORMULA
EXAMPLE
Array begins:
===================================================
m\n| 1 2 3 4 5 6 7 ...
---+-----------------------------------------------
1 | 0 1 3 6 10 15 21 ...
2 | 1 8 27 64 125 216 343 ...
3 | 3 27 126 426 1125 2493 4872 ...
4 | 6 64 426 2208 8830 27456 70434 ...
5 | 10 125 1125 8830 55700 265635 961975 ...
6 | 15 216 2493 27456 265635 2006280 11158161 ...
7 | 21 343 4872 70434 961975 11158161 98309778 ...
...
PROG
(PARI) T(m, n) = sum(j=1, min(m, n), j!^2*binomial(m, j)*binomial(n, j)*(1 + (m+n)/2 - j)) - m*n
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 24 2023
STATUS
approved