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A241544
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Number of partitions p of n such that (number of even numbers in p) is a part of p.
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2
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0, 0, 0, 1, 1, 3, 5, 7, 12, 17, 26, 34, 49, 66, 90, 118, 155, 203, 261, 337, 428, 546, 685, 863, 1075, 1345, 1664, 2060, 2538, 3118, 3816, 4661, 5680, 6901, 8368, 10111, 12207, 14690, 17656, 21155, 25326, 30238, 36058, 42901, 50973, 60438, 71568, 84586
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OFFSET
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0,6
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COMMENTS
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Each number in p is counted once, regardless of its multiplicity.
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LINKS
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EXAMPLE
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a(6) counts these 5 partitions: 42, 411, 321, 2211, 21111.
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MATHEMATICA
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z = 50; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0]; s1[p_] :=
Count[Mod[DeleteDuplicates[p], 2], 1];
Table[Count[f[n], p_ /; MemberQ[p, s0[p]]], {n, 0, z}] (* A241544 *)
Table[Count[f[n], p_ /; MemberQ[p, s1[p]]], {n, 0, z}] (* A241545 *)
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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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