A098490 Triangle T(n,k) read by rows: partitions of n with parts occurring at most thrice, k parts occurring once or twice and an odd number of parts.

0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 2, 3, 1, 0, 2, 4, 2, 1, 2, 4, 4, 0, 1, 7, 6, 0, 0, 3, 8, 7, 1, 1, 3, 9, 10, 2, 0, 4, 12, 12, 4, 0, 5, 14, 15, 7, 1, 3, 18, 23, 7, 1, 0, 6, 19, 26, 14, 1, 0, 7, 22, 32, 20, 2, 2, 6, 24, 42, 26, 4, 0, 8, 30, 49, 35, 7, 0, 8, 36, 60, 44

Offset: 0

Author

Ralf Stephan, Sep 12 2004

Keywords

• nonn
• tabf

Examples

			Triangle starts:
  {1}
  {0,1}
  {0,1}
  {1,1,0}
  {0,1,1}
  {0,1,2}
  {1,1,1,1}
  ...
6 is 2+2+2, 6, 1+1+4, 1+2+3, with odd number of parts and no part more than thrice. The number of parts occurring once or twice in these partitions is 0,1,2,3, respectively. The 6th row is therefore 1,1,1,1.
		

Links

• Alex Fink, Richard K. Guy, and Mark Krusemeyer, Partitions with parts occurring at most thrice, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114.

Crossrefs

Differs from A098489 in rows with triangular index. Cf. A094893.

Row sums are in A098492.