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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 30 00:49 EDT 2023. Contains 361599 sequences. (Running on oeis4.)