A233292 Triangle read by rows: T(n,k) is the number of partitions of n into at most four parts in which no part exceeds k, 0 <= k <= n.

1, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 3, 4, 5, 0, 0, 2, 4, 5, 6, 0, 0, 2, 5, 7, 8, 9, 0, 0, 1, 4, 7, 9, 10, 11, 0, 0, 1, 4, 8, 11, 13, 14, 15, 0, 0, 0, 3, 7, 11, 14, 16, 17, 18, 0, 0, 0, 2, 7, 12, 16, 19, 21, 22, 23, 0, 0, 0, 1, 5, 11, 16, 20, 23, 25, 26, 27, 0, 0, 0, 1, 5, 11, 18, 23, 27, 30, 32, 33, 34

Offset

0,6

Comments

Transpose of table A219237.

Links

Table of n, a(n) for n=0..90.

Formula

T(n,k) = Sum_{j=0..k} A232539(n,j).

Example

Triangle T(n,k) begins:
1;
0, 1;
0, 1, 2;
0, 1, 2, 3;
0, 1, 3, 4, 5;
0, 0, 2, 4, 5,  6;
0, 0, 2, 5, 7,  8,  9;
0, 0, 1, 4, 7,  9, 10, 11;
0, 0, 1, 4, 8, 11, 13, 14, 15; ...

Crossrefs

Cf. A001400 (main diagonal), A219237, A232539.

Sequence in context: A159880 A289251 A353174 * A108456 A089107 A361756

Adjacent sequences: A233289 A233290 A233291 * A233293 A233294 A233295

Keyword

nonn,tabl

Author

L. Edson Jeffery, Jan 02 2014

Status

approved