A392995 Number of plane partitions with multiplicities of parts matching the n-th composition in standard order.

1, 2, 2, 3, 4, 3, 4, 5, 7, 8, 10, 5, 7, 8, 10, 7, 12, 13, 18, 12, 20, 18, 26, 7, 12, 13, 18, 12, 20, 18, 26, 11, 19, 25, 34, 23, 37, 37, 52, 20, 34, 42, 58, 32, 52, 54, 76, 11, 19, 25, 34, 23, 37, 37, 52, 20, 34, 42, 58, 32, 52, 54, 76, 15, 30, 39, 56, 42, 72

Offset

1,2

Comments

a(n) is the number of normal generalized Young tableaux with rows and columns weakly decreasing (Cf. A299926), whose entries have multiplicities matching the n-th composition in standard order.

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..4096

John Tyler Rascoe, Python code.

Formula

a(2^k + j) = a(2^k + j + 2^(k-1)) for k > 0 and 0 <= j < 2^(k-1) - 1.

a(2^k-1) = A000085(k) for k > 0.

a(2^k) = A000041(k+1).

a(2^k+1) = A000070(k).

Example

The 5th composition in standard order (2,1) corresponds to plane partitions with 3 parts (a^2,b), so a(5) = 4:
  a a b   a a   a b   a
          b     a     a
                      b

Prog

(Python) # see links

Crossrefs

Cf. A000041, A000070, A000085, A000219, A066099, A299926, A379277.

Sequence in context: A357589 A336200 A032355 * A308597 A205153 A300302

Adjacent sequences: A392992 A392993 A392994 * A392996 A392997 A392998

Keyword

nonn

Author

John Tyler Rascoe, Jan 29 2026

Status

approved