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A182616
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Number of partitions of 2n that contain odd parts.
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7
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0, 1, 3, 8, 17, 35, 66, 120, 209, 355, 585, 946, 1498, 2335, 3583, 5428, 8118, 12013, 17592, 25525, 36711, 52382, 74173, 104303, 145698, 202268, 279153, 383145, 523105, 710655, 960863, 1293314, 1733281, 2313377, 3075425, 4073085, 5374806, 7067863, 9263076
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OFFSET
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0,3
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COMMENTS
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Bisection (even part) of A086543.
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LINKS
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Table of n, a(n) for n=0..38.
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FORMULA
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a(n) = A000041(2*n) - A000041(n).
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EXAMPLE
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For n=3 the partitions of 2n are
6 ....................... does not contains odd parts
3 + 3 ................... contains odd parts ........... *
4 + 2 ................... does not contains odd parts
2 + 2 + 2 ............... does not contains odd parts
5 + 1 ................... contains odd parts ........... *
3 + 2 + 1 ............... contains odd parts ........... *
4 + 1 + 1 ............... contains odd parts ........... *
2 + 2 + 1 + 1 ........... contains odd parts ........... *
3 + 1 + 1 + 1 ........... contains odd parts ........... *
2 + 1 + 1 + 1 + 1 ....... contains odd parts ........... *
1 + 1 + 1 + 1 + 1 + 1 ... contains odd parts ........... *
There are 8 partitions of 2n that contain odd parts.
Also p(2n)-p(n) = p(6)-p(3) = 11-3 = 8, where p(n) is the number of partitions of n, so a(3)=8.
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MAPLE
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with(combinat): a:= n-> numbpart(2*n) -numbpart(n): seq(a(n), n=0..35);
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CROSSREFS
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Cf. A000041, A086543, A304710.
Sequence in context: A182734 A327608 A239844 * A159217 A052996 A112523
Adjacent sequences: A182613 A182614 A182615 * A182617 A182618 A182619
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Dec 03 2010
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EXTENSIONS
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Edited by Alois P. Heinz, Dec 03 2010
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STATUS
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approved
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