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

1,7

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.

Links

Table of n, a(n) for n=1..88.

Example

--------------------------------------------------
.                        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.

Sequence in context: A268374 A204263 A228347 * A079632 A002654 A113652

Adjacent sequences: A209311 A209312 A209313 * A209315 A209316 A209317

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 20 2013

Status

approved