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A213368 Row sums of triangle A212954 of two color Ramsey numbers. 1

%I

%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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Last modified January 17 12:18 EST 2020. Contains 330958 sequences. (Running on oeis4.)