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A239263
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Number of partitions of n having (sum of odd parts) >= (sum of even parts).
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5
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1, 1, 1, 2, 3, 5, 6, 8, 14, 19, 24, 30, 49, 61, 75, 93, 144, 177, 217, 260, 385, 461, 556, 663, 956, 1137, 1353, 1603, 2222, 2625, 3093, 3622, 4956, 5796, 6790, 7907, 10578, 12299, 14283, 16558, 21830, 25269, 29175, 33607, 43656, 50227, 57723, 66199, 85183
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(8) counts these 14 partitions: 71, 53, 521, 5111, 431, 41111, 332, 3311, 3221, 32111, 311111, 221111, 2111111, 11111111.
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MATHEMATICA
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z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
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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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