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A306318
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Number of square twice-partitions of n.
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3
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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
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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EXAMPLE
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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))
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MATHEMATICA
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Table[Sum[Length[Union@@(Tuples[IntegerPartitions[#, {k}]&/@#]&/@IntegerPartitions[n, {k}])], {k, 0, Sqrt[n]}], {n, 0, 20}]
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Feb 07 2019
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STATUS
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approved
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