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

0,4

Comments

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

Links

Table of n, a(n) for n=0..31.

Formula

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

Example

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.

Sequence in context: A095350 A084776 A162921 * A291732 A291264 A171849

Adjacent sequences: A237042 A237043 A237044 * A237046 A237047 A237048

Keyword

nonn

Author

Omar E. Pol, Feb 02 2014

Status

approved