A237047 Number of compositions of n minus the number of overpartitions of n.

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

Author

Omar E. Pol, Feb 02 2014

Keywords

• sign

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A011782, A015128, A056823, A230441, A236633, A237044, A237045.

Formula

a(n) = A011782(n) - A015128(n).