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| NAME
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allocatedNumber of partitions p of n such that (sum of parts with multiplicity 1) >= (sum of forall Clarkother Kimberlingparts).
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| DATA
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1, 1, 1, 2, 3, 4, 6, 8, 13, 17, 22, 28, 43, 55, 71, 87, 124, 153, 202, 243, 332, 401, 511, 608, 828, 984, 1236, 1458, 1903, 2245, 2826, 3301, 4245, 4963, 6119, 7108, 9064, 10508, 12837, 14834, 18584, 21442, 26150, 30028, 37139, 42599, 51356, 58742, 72370
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| OFFSET
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0,4
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| FORMULA
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a(n) + A240449(n) = A000041(n) for n >= 0.
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| EXAMPLE
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a(6) counts these 6 partitions: 6, 51, 42, 411, 321, 3111.
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| MATHEMATICA
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z = 30; p[n_] := p[n] = IntegerPartitions[n]; f[p_] := f[p] = First[Transpose[p]];
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] < n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240448 *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] <= n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240449 *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] == n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240447 with alternating 0s *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] > n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240451 *)
ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] >= n &], {n, 0, z}]] (* shows the partitions *)
Map[Length, t] (* A240452 *)
(* Peter J. C. Moses, Apr 02 2014 *)
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| CROSSREFS
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Cf. A240448, A240447, A240449, A240451, A000041.
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| KEYWORD
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allocated
nonn,easy
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| AUTHOR
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Clark Kimberling, Apr 05 2014
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| STATUS
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approved
editing
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