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A238793
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Number of palindromic partitions of n such that 2*(multiplicity of least part) = (multiplicity of greatest part).
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2
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0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 3, 1, 3, 3, 6, 5, 6, 5, 9, 9, 13, 10, 17, 13, 23, 18, 29, 23, 37, 32, 48, 37, 64, 48, 81, 60, 99, 77, 130, 94, 158, 123, 200, 145, 252, 182, 309, 224, 381, 277, 475, 331, 575, 414, 712, 497, 866, 605, 1049, 736, 1274, 883, 1555
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OFFSET
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1,10
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COMMENTS
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Palindromic partitions are defined at A025065.
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LINKS
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EXAMPLE
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a(15) counts these 6 partitions (written as palindromes): 717, 636, 25152, 13431, 12233221..
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MATHEMATICA
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z = 65; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (2*Count[#, Min[#]] == Count[#, Max[#]]) &]; Table[p[n], {n, 1, 16}]
t1 = Table[Length[p[n]], {n, 1, z}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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