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

0,14

Links

Table of n, a(n) for n=0..89.

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.

Example

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.

Crossrefs

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

Row sums are in A098492.

Sequence in context: A342788 A059883 A086967 * A247138 A212627 A029419

Adjacent sequences: A098487 A098488 A098489 * A098491 A098492 A098493

Keyword

nonn,tabf

Author

Ralf Stephan, Sep 12 2004

Status

approved