A292776 Triangle read by rows: row n gives number of Ramsey partitions of n+k (2 <= k <= n).

3, 2, 5, 4, 3, 11, 3, 4, 5, 14, 5, 7, 11, 7, 31, 4, 5, 8, 10, 11, 34, 6, 6, 19, 11, 24, 15, 69, 5, 9, 11, 12, 25, 22, 22, 82, 7, 7, 20, 21, 33, 23, 49, 30, 139

Offset

2,1

Comments

See McAvaney et al. for definition of Ramsey partition: If k1 and k2 are positive integers, the partition P = (p1,p2,...,pn) of k1+k2 is said to be a Ramsey partition for the pair k1, k2 if for any sublist L of P, either there is a sublist of L which sums to k1 or a sublist of P -L which sums to k2.

Links

Table of n, a(n) for n=2..46.

Kevin McAvaney, Jack Robertson, and William Webb, Ramsey partitions of integers and fair divisions, Combinatorica 12, pp. 193-201 (1992).

Example

Triangle begins:
  3;
  2,  5;
  4,  3, 11;
  3,  4,  5, 14;
  5,  7, 11,  7, 31;
  4,  5,  8, 10, 11, 34;
  6,  6, 19, 11, 24, 15, 69;
  5,  9, 11, 12, 25, 22, 22, 82;
  7,  7, 20, 21, 33, 23, 49, 30, 139;
  ...

Crossrefs

Sequence in context: A128076 A076243 A140061 * A061313 A259846 A087669

Adjacent sequences: A292773 A292774 A292775 * A292777 A292778 A292779

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Oct 01 2017

Status

approved