A394348 Number of rectangular plane partitions of n with exactly 3 rows and with rows and columns strictly decreasing.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 19, 24, 30, 37, 49, 60, 78, 98, 125, 155, 199, 243, 306, 376, 466, 566, 700, 844, 1033, 1246, 1513, 1817, 2203, 2636, 3180, 3808, 4575, 5464, 6557, 7815, 9347, 11132, 13274, 15774, 18773, 22255, 26409, 31257, 36986, 43667, 51557

Offset

0,9

Links

Table of n, a(n) for n=0..57.

Formula

G.f.: Sum_{k>=1} q^(3*k*(k+3)/2) * Product_{i=1..3} Product_{j=1..k} 1/(1 - q^(i+j-1)).

Example

The a(10) = 4 matrices:
  [7] [6] [5] [5]
  [2] [3] [4] [3]
  [1] [1] [1] [2]

Prog

(PARI) my(N=60, q='q+O('q^N)); concat([0, 0, 0, 0, 0, 0], Vec(sum(k=1, N, q^(3*k*(k+3)/2)*prod(i=1, 3, prod(j=1, k, 1/(1-q^(i+j-1)))))))

Crossrefs

Column k=3 of A394187.

Cf. A323430, A395925.

Sequence in context: A029003 A339279 A034296 * A075745 A214036 A100289

Adjacent sequences: A394344 A394345 A394346 * A394349 A394350 A394351

Keyword

nonn

Author

Seiichi Manyama, May 10 2026

Status

approved