OFFSET
1,5
COMMENTS
Essentially the same as A059442, which is the main entry for these numbers.
REFERENCES
See A059442.
LINKS
Stanislaw Radziszowski, Small Ramsey Numbers, The Electronic Journal of Combinatorics, Dynamic Surveys, DS1, Mar 3 2017.
Fabrizio Tamburini, Random-projector quantum diagnostics of Ramsey numbers and a prime-factor heuristic for R(5,5)=45, arXiv:2508.16699 [quant-ph], 2025. See references.
Eric Weisstein's World of Mathematics, Ramsey Number
Wikipedia, Ramsey's theorem
FORMULA
R(r, 1) = R(1, r) = 1
R(r, 2) = R(2, r) = r
R(r, s) <= R(r-1, s) + R(r, s-1)
R(r, s) <= R(r-1, s) + R(r, s-1) - 1 if R(r-1, s) and R(r, s-1) are both even
R(r, r) <= 4 * R(r, r-2) + 2
EXAMPLE
The initial antidiagonals are:
1,
1, 1,
1, 2, 1,
1, 3, 3, 1,
1, 4, 6, 4, 1,
1, 5, 9, 9, 5, 1,
1, 6, 14, 18, 14, 6, 1,
1, 7, 18, 25, 25, 18, 7, 1,
1, 8, 23, ?, ?, ?, 23, 8, 1,
1, 9, 28, ?, ?, ?, ?, 28, 9, 1,
1, 10, 36, ?, ?, ?, ?, ?, 36, 10, 1,
...
CROSSREFS
KEYWORD
AUTHOR
Joerg Arndt, Jun 01 2012
EXTENSIONS
Edited by N. J. A. Sloane, Nov 05 2023
STATUS
approved