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A091915
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Maximum of even products of partitions of n.
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1
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0, 2, 2, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, 4374, 5832, 8748, 13122, 17496, 26244, 39366, 52488, 78732, 118098, 157464, 236196, 354294, 472392, 708588, 1062882, 1417176, 2125764, 3188646, 4251528
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OFFSET
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1,2
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LINKS
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FORMULA
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For n>6, a(n+3) = 3a(n) (conjectured). - Ralf Stephan, Dec 02 2004
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EXAMPLE
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The partitions of 5 are 5, 41, 32, 311, 221, 2111, 11111, with products 5, 4, 6, 3, 4, 2, 1 and the maximal even product is 6.
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MATHEMATICA
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first Needs["DiscreteMath`Combinatorica`"], then f[n_] := Max[ Select[ Apply[ Times, Partitions[n], 2], EvenQ[ # ] &]]; Table[ f[n], {n, 1, 42}] (* Robert G. Wilson v, Feb 12 2004 *)
Join[{0}, Table[Max[Select[Times@@@IntegerPartitions[n], EvenQ]], {n, 2, 50}]] (* Harvey P. Dale, Jan 17 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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