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A371736
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Number of non-quanimous strict integer partitions of n, meaning no set partition with more than one block has all equal block-sums.
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14
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1, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 12, 11, 18, 15, 26, 23, 38, 30, 54, 43, 72, 57, 104, 77, 142, 102, 179, 138, 256, 170, 340, 232, 412, 292, 585, 365, 760, 471, 889, 602, 1260, 718, 1610, 935, 1819, 1148, 2590, 1371, 3264, 1733, 3581, 2137, 5120, 2485, 6372
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OFFSET
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0,4
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COMMENTS
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A finite multiset of numbers is defined to be quanimous iff it can be partitioned into two or more multisets with equal sums. Quanimous partitions are counted by A321452 and ranked by A321454.
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(9) = 8 strict partitions:
() (1) (2) (3) (4) (5) (6) (7) (8) (9)
(21) (31) (32) (42) (43) (53) (54)
(41) (51) (52) (62) (63)
(61) (71) (72)
(421) (521) (81)
(432)
(531)
(621)
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[Select[sps[#], SameQ@@Total/@#&]]==1&]], {n, 0, 30}]
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CROSSREFS
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A371783 counts k-quanimous partitions.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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