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A237047
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Number of compositions of n minus the number of overpartitions of n.
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3
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0, -1, -2, -4, -6, -8, -8, 0, 28, 102, 280, 680, 1544, 3368, 7152, 14912, 30706, 62672, 127124, 256744, 516952, 1038672, 2083864, 4176576, 8365080, 16746150, 33513608, 67055456, 134148160, 268345208, 536754288, 1073591680, 2147291036, 4294721040, 8589620784
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OFFSET
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0,3
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COMMENTS
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Note that a(7) = 0 therefore 7 is the only positive integer whose number of compositions equals the number of overpartitions: A011782(7) = A015128(7) = 64.
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LINKS
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FORMULA
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EXAMPLE
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Illustration of a(4) = -6.
--------------------------------------------------------
. Compositions of 4 Overpartitions of 4
--------------------------------------------------------
. _ _ _ _ _ _ _ _
1 |_| | | | 1, 1, 1, 1 |.| | | | 1', 1, 1, 1
2 |_ _| | | 2, 1, 1 |_| | | | 1, 1, 1, 1
3 |_| | | 1, 2, 1 | .|.| | 2', 1', 1
4 |_ _ _| | 3, 1 | |.| | 2, 1', 1
5 |_| | | 1, 1, 2 | .| | | 2', 1, 1
6 |_ _| | 2, 2 |_ _| | | 2, 1, 1
7 |_| | 1, 3 | .|.| 3', 1
8 |_ _ _ _| 4 | |.| 3, 1
9 | .| | 3', 1
10 |_ _ _| | 3, 1
11 | .| | 2', 2
12 |_ _| | 2, 2
13 | .| 4'
14 |_ _ _ _| 4
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There are 8 compositions of 4 and there are 14 overpartitions of 4, so a(4) = 8 - 14 = -6.
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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