A393786 Number of cyclically symmetric planar subpartitions of the size n pyramidal planar partition.

1, 2, 3, 6, 23, 88, 443, 3960, 38959, 506642, 11160832, 284581172, 9639057994

Offset

0,2

Comments

The planar partition having its subpartitions counted is:

n n-1 ... 2 1

n-1 n-2 ... 1

... ...

2 1

1

A planar partition is said to be totally symmetric if it is invariant by the action of the cyclic group C_3.

The number of all subpartitions regardless of symmetry is given by A115965.

The number of symmetric subpartitions is given by A388969.

The number of totally symmetric subpartitions is given by A393748.

Links

Table of n, a(n) for n=0..12.

Ludovic Schwob, SageMath program

Example

The a(4) = 23 cyclically symmetric planar subpartitions of the pyramidal planar partition of size 4 are:
  Ø        1        21       22       22       311      321      321
                    1        21       22       1        21       22
                                               1        1        1
.
  332      332      331      322      331      322      4111     4211
  311      321      211      31       221      32       1        2
  21       21       2        11       2        11       1        1
                                                        1        1
.
  4211     4321     4321     4311     4221     4311     4221
  22       311      321      211      31       221      32
  1        21       21       2        11       2        11
  1        1        1        1        1        1        1

Prog

(SageMath) # See Links

Crossrefs

Cf. A006366, A115965, A388969, A393748.

Sequence in context: A183179 A018300 A317973 * A361333 A327013 A171708

Adjacent sequences: A393783 A393784 A393785 * A393787 A393788 A393789

Keyword

nonn,more

Author

Ludovic Schwob, Feb 27 2026

Status

approved