A237044
Number of overcompositions of n minus the number of partitions of n.
Original entry on oeis.org
0, 1, 2, 9, 21, 53, 133, 309, 706, 1572, 3534, 7752, 16991, 36807, 79385, 170528, 364563, 776739, 1649071, 3490698, 7366917, 15512544, 32583646, 68306009, 142902505, 298446956, 622232624, 1295316994, 2692580198, 5589582431, 11588900240, 23999045850
Offset: 0
A237047
Number of compositions of n minus the number of overpartitions of n.
Original entry on oeis.org
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
Offset: 0
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
.
There are 8 compositions of 4 and there are 14 overpartitions of 4, so a(4) = 8 - 14 = -6.
A237272
Number of overcompositions of n that contain at least two parts in increasing order and that contain at least one overlined part.
Original entry on oeis.org
0, 0, 0, 3, 9, 27, 83, 211, 522, 1222, 2874, 6496, 14593, 32185, 70423, 153024, 330195, 708933, 1514821, 3224134, 6836547, 14455648, 30475210, 64096487, 134493519, 281642590, 588642240, 1228160742, 2558300338, 5321065857, 11051923912, 22925167566
Offset: 0
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