A209314 Tetrahedron T(n,k,j) of appearances of k as the smallest parts in all partition of n.

1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 3, 1, 1, 0, 0, 0, 1, 1, 1, 2, 3, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 5, 7, 1, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 5, 7, 11, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3

Offset: 1

Author

Omar E. Pol, Jan 20 2013

Keywords

• nonn
• tabf

Comments

The sum of row k of the slice n is A220504(n,k).

The sum of all elements of the n-th slice is spt(n) = A092269(n), the smallest parts partition function.

First row of slice n lists the first n partition numbers A000041.

Examples

			--------------------------------------------------
.                        Triangle
Tetrahedron              A220504       A092269(n)
(Slice n = 1..6)      (the row sums)     spt(n)
--------------------------------------------------
1;                           1             1
--------------------------------------------------
1, 1;                        2
1;                           1             3
--------------------------------------------------
1, 1, 2;                     4
0, 0;                        0
1;                           1             5
--------------------------------------------------
1, 1, 2, 3;                  7
1, 1, 0;                     2
0, 0;                        0
1;                           1            10
--------------------------------------------------
1, 1, 2, 3, 5;              12
0, 1, 0, 0;                  1
0, 0, 0;                     0
0, 0;                        0
1;                           1            14
--------------------------------------------------
1, 1, 2, 3, 5, 7;           19
1, 1, 2, 0, 0;               4
1, 1, 0, 0;                  2
0, 0, 0;                     0
0, 0;                        0
1;                           1            26
--------------------------------------------------
		

Crossrefs

Cf. A000041, A092269, A220504.