A306318 Number of square twice-partitions of n.

1, 1, 1, 1, 2, 2, 4, 5, 10, 12, 19, 24, 39, 49, 73, 104, 151, 212, 317, 443, 638, 936, 1296, 1841, 2635, 3641, 5069, 7176, 9884, 13614, 19113, 26162, 36603, 50405, 70153, 96176, 135388, 184753, 257882, 353587, 494653, 671992, 934905, 1272195, 1762979, 2389255

Offset

0,5

Comments

A twice partition of n is a sequence of integer partitions, one of each part in an integer partition of n. It is square if the number of parts is equal to the number of parts in each part.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

The a(10) = 19 square twice-partitions:
  ((ten))  ((32)(32))  ((211)(111)(111))
           ((32)(41))
           ((33)(22))
           ((33)(31))
           ((41)(32))
           ((41)(41))
           ((42)(22))
           ((42)(31))
           ((43)(21))
           ((44)(11))
           ((51)(22))
           ((51)(31))
           ((52)(21))
           ((53)(11))
           ((61)(21))
           ((62)(11))
           ((71)(11))

Mathematica

Table[Sum[Length[Union@@(Tuples[IntegerPartitions[#, {k}]&/@#]&/@IntegerPartitions[n, {k}])], {k, 0, Sqrt[n]}], {n, 0, 20}]

Crossrefs

Cf. A000219, A001970, A063834 (twice-partitions), A089299 (square plane partitions), A279787, A305551, A306017, A306319 (rectangular twice-partitions), A319066, A323429, A323531 (square partitions of partitions).

Sequence in context: A135586 A168542 A116646 * A091188 A147678 A195865

Adjacent sequences: A306315 A306316 A306317 * A306319 A306320 A306321

Keyword

nonn

Author

Gus Wiseman, Feb 07 2019

Status

approved