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
Examples
-------------------------------------------------------- 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.