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A306318
Number of square twice-partitions of n.
3
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 07 2019
STATUS
approved