A236626
Sum of all parts of all overcompositions of n.
Original entry on oeis.org
2, 8, 36, 104, 300, 864, 2268, 5824, 14418, 35760, 85888, 204816, 479804, 1113280, 2560560, 5836704, 13209612, 29690208, 66332572, 147350880, 325780056, 716862256, 1571067072, 3429697920, 7461222850, 16178111560, 34973640108, 75392349648
Offset: 1
For n = 3 the 12 overcompositions of 3 are [3], [3'], [1, 2], [1', 2], [1, 2'], [1', 2'], [2, 1], [2', 1], [2, 1'], [2', 1'], [1, 1, 1], [1', 1, 1], hence the sum of all parts is 3+3+1+2+1+2+1+2+1+2+2+1+2+1+2+1+2+1+1+1+1+1+1+1 = 3*12 = 36, so a(3) = 36.
A236628
Triangle read by rows in which T(n,k) is the number of parts in the k-th region of the set of overcompositions of n, with overcompositions in colexicographic order.
Original entry on oeis.org
2, 2, 4, 2, 6, 4, 12, 2, 6, 4, 14, 4, 6, 4, 26
Offset: 1
Written as an irregular triangle in which row n has length 2^n the sequence begins:
2;
2, 4;
2, 6, 4, 12;
2, 6, 4, 14, 4, 6, 4, 26;
...
For n = 3 the diagram shows the four regions of the overcompositions of 3, with overcompositions in colexicographic order.
------------------------------------------------
. Diagram of Regions of the diagram
overcompositions ------------------------
. of 3 k: 1 2 3 4
------------------------------------------------
. _ _ _ _ _ _
1 |.| | | |.| | | | |
2 |_| | | |_| _| | | |
3 | .|.| | .| |.|
4 | |.| | | |.|
5 | .| | | .| | |
6 |_ _| | |_ _| _ _| |
7 |.| .| |.| | .|
8 | | .| | | | .|
9 |.| | |.| | |
10 |_| | |_| _| |
11 | .| | .|
12 |_ _ _| |_ _ _|
...
Number of parts.........: 2 6 4 12
.
Every row of every region contains only one part.
Showing 1-2 of 2 results.
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