This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212954 #48 Feb 16 2025 08:33:17 %S A212954 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, %T A212954 25,18,7,1,1,8,23 %N A212954 Array of Ramsey numbers R(n,k) (n >= 1, k >= 1) read by antidiagonals. %C A212954 Essentially the same as A059442, which is the main entry for these numbers. %D A212954 See A059442. %H A212954 Stanislaw Radziszowski, <a href="https://doi.org/10.37236/21">Small Ramsey Numbers</a>, The Electronic Journal of Combinatorics, Dynamic Surveys, DS1, Mar 3 2017. %H A212954 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamseyNumber.html">Ramsey Number</a> %H A212954 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ramsey_theorem">Ramsey's theorem</a> %F A212954 R(r, 1) = R(1, r) = 1 %F A212954 R(r, 2) = R(2, r) = r %F A212954 R(r, s) <= R(r-1, s) + R(r, s-1) %F A212954 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 %F A212954 R(r, r) <= 4 * R(r, r-2) + 2 %e A212954 The initial antidiagonals are: %e A212954 1, %e A212954 1, 1, %e A212954 1, 2, 1, %e A212954 1, 3, 3, 1, %e A212954 1, 4, 6, 4, 1, %e A212954 1, 5, 9, 9, 5, 1, %e A212954 1, 6, 14, 18, 14, 6, 1, %e A212954 1, 7, 18, 25, 25, 18, 7, 1, %e A212954 1, 8, 23, ?, ?, ?, 23, 8, 1, %e A212954 1, 9, 28, ?, ?, ?, ?, 28, 9, 1, %e A212954 1, 10, 36, ?, ?, ?, ?, ?, 36, 10, 1, %e A212954 ... %e A212954 ... %Y A212954 Cf. A000791, A213368 (row sums). %K A212954 nonn,tabl,hard,more %O A212954 1,5 %A A212954 _Joerg Arndt_, Jun 01 2012 %E A212954 Edited by _N. J. A. Sloane_, Nov 05 2023