A210960 Tetrahedron T(j,n,k) in which the slice j is a finite triangle read by rows T(n,k) which list the number of parts in the columns of the shell model of partitions with n shells mentioned in A210970.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 3, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 3, 4, 3, 2, 1, 1, 1, 3, 4, 3, 2, 1, 1

Offset

1,14

Links

Table of n, a(n) for n=1..84.

Example

--------------------------------------------------------
Illustration of first five
slices of the tetrahedron                       Row sum
--------------------------------------------------------
. 1,                                               1
.    1,                                            1
.    1, 1,                                         2
.          1,                                      1
.          1, 1,                                   2
.          1, 1, 1,                                3
.                   1,                             1
.                   1, 1,                          2
.                   2, 1, 1,                       4
.                   1, 2, 1, 1,                    5
.                               1,                 1
.                               1, 1,              2
.                               2, 1, 1,           4
.                               2, 2, 1, 1,        6
.                               1, 2, 2, 1, 1,     7
--------------------------------------------------------
. 1, 2, 1, 3, 2, 1, 5, 4, 2, 1, 7, 6, 4, 2, 1,
.
It appears that column sums give A058399.
Also, written as a triangle read by rows in which each row is a flattened triangle, begins:
1;
1,1,1,
1,1,1,1,1,1;
1,1,1,2,1,1,1,2,1,1;
1,1,1,2,1,1,2,2,1,1,1,2,2,1,1;
1,1,1,2,1,1,3,2,1,1,3,3,2,1,1,1,3,3,2,1,1;
1,1,1,2,1,1,3,2,1,1,4,3,2,1,1,3,4,3,2,1,1,1,3,4,3,2,1,1;
In which row sums give A006128.

Crossrefs

Cf. A058399, A135010, A138121, A182703, A209655, A209918, A210763, A210961.

Sequence in context: A062557 A276438 A338274 * A339095 A193509 A331284

Adjacent sequences: A210957 A210958 A210959 * A210961 A210962 A210963

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 22 2012

Status

approved