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

1, 2, 4, 8, 16, 30, 60, 102

Offset: 1

Author

Omar E. Pol, Jun 10 2012

Keywords

• nonn
• hard
• more

Comments

The next terms is known to be in the range 179-195.

Examples

			Since the triangle A212954 is symmetric we can write:
a(1)  = 1.
a(2)  = 2*1 = 2.
a(3)  = 2*1+2 = 2+2 = 4.
a(4)  = 2*(1+3) = 2*4 = 8.
a(5)  = 2*(1+4)+6 = 2*5+6 = 10+6 = 16.
a(6)  = 2*(1+5+9) = 2*15 = 30.
a(7)  = 2*(1+6+14)+18 = 2*21+18 = 42+18 = 60.
a(8)  = 2*(1+7+18+25) = 2*51 = 102.
And for the next three known terms we can write:
a(9)  = 2*(1+8+23+ ?)+ ? = ?.
a(10) = 2*(1+9+28+ ?+ ?) = ?.
a(11) = 2*(1+10+36+ ?+ ?)+ ? = ?.
		

Links

• Eric Weisstein's World of Mathematics, Ramsey Number
• Wikipedia, Ramsey's theorem

Crossrefs

Cf. A000791, A059442, A212954.