A194702 Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (2 + m).

2, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1

Offset

1,1

Comments

Sub-triangle of A182703 and also of A194812. Note that the sum of every row is also the number of partitions of 2. For further information see A182703 and A135010.

Links

Table of n, a(n) for n=1..91.

Formula

T(k,m) = A182703(2+m,k), with T(k,m) = 0 if k > 2+m.

T(k,m) = A194812(2+m,k).

Example

Triangle begins:
2,
0, 2,
1, 0, 1,
0, 1, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
...
For k = 1 and  m = 1; T(1,1) = 2 because there are two parts of size 1 in the last section of the set of partitions of 3, since 2 + m = 3, so a(1) = 2. For k = 2 and m = 1; T(2,1) = 0 because there are no parts of size 2 in the last section of the set of partitions of 3, since 2 + m = 3, so a(2) = 0.

Crossrefs

Always the sum of row k = p(2) = A000041(n) = 2.

The first (0-10) members of this family of triangles are A023531, A129186, this sequence, A194703-A194710.

Cf. A135010, A138121, A182712-A182714, A194812.

Sequence in context: A072627 A277144 A069848 * A118682 A198393 A083054

Adjacent sequences: A194699 A194700 A194701 * A194703 A194704 A194705

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 05 2012

Status

approved