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 A213368 #24 Feb 16 2025 08:33:17 %S A213368 1,2,4,8,16,30,60,102 %N A213368 Row sums of triangle A212954 of two color Ramsey numbers. %C A213368 The next terms is known to be in the range 179-195. %H A213368 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamseyNumber.html">Ramsey Number</a> %H A213368 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ramsey_theorem">Ramsey's theorem</a> %e A213368 Since the triangle A212954 is symmetric we can write: %e A213368 a(1) = 1. %e A213368 a(2) = 2*1 = 2. %e A213368 a(3) = 2*1+2 = 2+2 = 4. %e A213368 a(4) = 2*(1+3) = 2*4 = 8. %e A213368 a(5) = 2*(1+4)+6 = 2*5+6 = 10+6 = 16. %e A213368 a(6) = 2*(1+5+9) = 2*15 = 30. %e A213368 a(7) = 2*(1+6+14)+18 = 2*21+18 = 42+18 = 60. %e A213368 a(8) = 2*(1+7+18+25) = 2*51 = 102. %e A213368 And for the next three known terms we can write: %e A213368 a(9) = 2*(1+8+23+ ?)+ ? = ?. %e A213368 a(10) = 2*(1+9+28+ ?+ ?) = ?. %e A213368 a(11) = 2*(1+10+36+ ?+ ?)+ ? = ?. %Y A213368 Cf. A000791, A059442, A212954. %K A213368 nonn,hard,more %O A213368 1,2 %A A213368 _Omar E. Pol_, Jun 10 2012