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%I #23 Jun 19 2012 12:09:10
%S 1,2,4,8,16,30,60,102
%N Row sums of triangle A212954 of two color Ramsey numbers.
%C The next terms is known to be in the range 179-195.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamseyNumber.html">Ramsey Number</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ramsey_theorem">Ramsey's theorem</a>
%e Since the triangle A212954 is symmetric we can write:
%e a(1) = 1.
%e a(2) = 2*1 = 2.
%e a(3) = 2*1+2 = 2+2 = 4.
%e a(4) = 2*(1+3) = 2*4 = 8.
%e a(5) = 2*(1+4)+6 = 2*5+6 = 10+6 = 16.
%e a(6) = 2*(1+5+9) = 2*15 = 30.
%e a(7) = 2*(1+6+14)+18 = 2*21+18 = 42+18 = 60.
%e a(8) = 2*(1+7+18+25) = 2*51 = 102.
%e And for the next three known terms we can write:
%e a(9) = 2*(1+8+23+ ?)+ ? = ?.
%e a(10) = 2*(1+9+28+ ?+ ?) = ?.
%e a(11) = 2*(1+10+36+ ?+ ?)+ ? = ?.
%Y Cf. A000791, A059442, A212954.
%K nonn,hard,more
%O 1,2
%A _Omar E. Pol_, Jun 10 2012
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