A392357 Triangle read by rows: T(n,k) is the number of plane partitions of n with k smallest parts.

1, 0, 1, 0, 1, 2, 0, 3, 0, 3, 0, 3, 5, 0, 5, 0, 9, 3, 5, 0, 7, 0, 9, 13, 8, 7, 0, 11, 0, 22, 14, 17, 7, 11, 0, 15, 0, 26, 37, 17, 32, 11, 15, 0, 22, 0, 54, 35, 60, 27, 39, 15, 22, 0, 30, 0, 65, 99, 57, 82, 46, 57, 22, 30, 0, 42, 0, 131, 110, 143, 89, 121, 57, 80, 30, 42, 0, 56

Offset

0,6

Links

Table of n, a(n) for n=0..77.

John Tyler Rascoe, PARI code.

Example

Triangle begins:
     k=0   1   2   3   4   5   6   7   8
  n=0 [1],
  n=1 [0,  1],
  n=2 [0,  1,  2],
  n=3 [0,  3,  0,  3],
  n=4 [0,  3,  5,  0,  5],
  n=5 [0,  9,  3,  5,  0,  7],
  n=6 [0,  9, 13,  8,  7,  0, 11],
  n=7 [0, 22, 14, 17,  7, 11,  0, 15],
  n=8 [0, 26, 37, 17, 32, 11, 15,  0, 22],
  ...
T(4,1) = 3:  4   3 1   3
                       1
.
T(4,2) = 5:  2 2   2   2 1 1   2 1   2
                   2           1     1
                                     1
.
T(4,4) = 5:  1 1 1 1   1 1 1   1 1   1 1   1
                       1       1 1   1     1
                                     1     1
                                           1

Prog

(PARI) \\ see links

Crossrefs

Cf. A000041 (main diagonal), A000219 (row sums), A091298, A392995.

Sequence in context: A161123 A035442 A213177 * A265017 A349136 A035376

Adjacent sequences: A392354 A392355 A392356 * A392358 A392359 A392360

Keyword

nonn,tabl

Author

John Tyler Rascoe, Feb 05 2026

Status

approved