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

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Ramsey Number

Wikipedia, Ramsey's theorem

Example

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+ ?+ ?)+ ? = ?.

Crossrefs

Cf. A000791, A059442, A212954.

Sequence in context: A335542 A027423 A140410 * A216212 A164263 A283836

Adjacent sequences: A213365 A213366 A213367 * A213369 A213370 A213371

Keyword

nonn,hard,more

Author

Omar E. Pol, Jun 10 2012

Status

approved