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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.

A213368 Row sums of triangle A212954 of two color Ramsey numbers.

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%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