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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 07 2019
STATUS
approved