A237045 Number of overcompositions of n minus the number of overpartitions of n.

0, 0, 0, 4, 12, 36, 104, 260, 628, 1448, 3344, 7464, 16564, 36180, 78480, 169232, 362732, 774172, 1645508, 3485788, 7360208, 15503432, 32571360, 68289536, 142880552, 298417848, 622194236, 1295266596, 2692514348, 5589496748, 11588789220, 23998902548

Offset: 0

Author

Omar E. Pol, Feb 02 2014

Keywords

• nonn

Comments

Number of overcompositions of n that contain at least two parts in increasing order.

Examples

			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.
		

Crossrefs

Cf. A000041, A011782, A015128, A056823, A230441, A236002, A236633, A237044, A237047, A237272.

Formula

a(n) = A236002(n) - A015128(n).