This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Illustration of a(4) = -6 with both overcompositions and overpartitions in colexicographic order. -------------------------------------------------------- . Overcompositions of 4 Overpartitions of 4 -------------------------------------------------------- . _ _ _ _ _ _ _ _ 1 |.| | | | 1', 1, 1, 1 |.| | | | 1', 1, 1, 1 2 |_| | | | 1, 1, 1, 1 |_| | | | 1, 1, 1, 1 3 | .|.| | 2', 1', 1 | .|.| | 2', 1', 1 4 | |.| | 2, 1', 1 | |.| | 2, 1', 1 5 | .| | | 2', 1, 1 | .| | | 2', 1, 1 6 |_ _| | | 2, 1, 1 |_ _| | | 2, 1, 1 7 *|.| .| | 1', 2', 1 | .|.| 3', 1 8 *| | .| | 1, 2', 1 | |.| 3, 1 9 *|.| | | 1', 2, 1 | .| | 3', 1 10 *|_| | | 1, 2, 1 |_ _ _| | 3, 1 11 | .|.| 3', 1' | .| | 2', 2 12 | |.| 3, 1' |_ _| | 2, 2 13 | .| | 3', 1 | .| 4' 14 |_ _ _| | 3, 1 |_ _ _ _| 4 15 *|.| | .| 1', 1, 2' 16 *| | | .| 1, 1, 2' 17 *|.| | | 1', 1, 2 18 *|_| | | 1, 1, 2 19 | .| | 2', 2 20 |_ _| | 2, 2 21 *|.| .| 1', 3' 22 *| | .| 1, 3' 23 *|.| | 1', 3 24 *|_| | 1, 3 25 | .| 4' 26 |_ _ _ _| 4 . There are 26 overcompositions of 4 and there are 14 overpartitions of 4, so the difference is a(4) = 26 - 14 = 12. On the other hand there are 12 overcompositions of 4 that contain at least two parts in increasing order, so a(4) = 12.
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