A098489 Triangle T(n,k) read by rows: partitions of n with parts occurring at most thrice, k parts occurring once or twice and an even number of parts.

1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 3, 0, 0, 2, 3, 1, 0, 2, 4, 2, 1, 2, 4, 4, 0, 4, 7, 3, 1, 0, 3, 8, 7, 1, 1, 3, 9, 10, 2, 0, 4, 12, 12, 4, 0, 5, 14, 15, 7, 2, 5, 13, 21, 11, 0, 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

Offset

0,14

Links

Table of n, a(n) for n=0..88.

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 begins:
  {1}
  {0,0}
  {0,1}
  {0,0,1}
  {0,1,1}
  {0,1,2}
  {0,2,3,0}
  ...
6 is 1+1+1+3, 1+1+2+2, 1+5, 2+4, 3+3 with even number of parts and no part more than thrice. Two of these partitions have one part occurring once or twice and (the middle) three have two such parts. The 6th row is therefore 0,2,3,0.

Crossrefs

Differs from A098490 in rows with triangular index. Cf. A098493.

Row sums are in A098491.

Sequence in context: A307391 A129883 A293578 * A128064 A144217 A187881

Adjacent sequences: A098486 A098487 A098488 * A098490 A098491 A098492

Keyword

nonn,tabf

Author

Ralf Stephan, Sep 12 2004

Status

approved