|
|
A210980
|
|
Total area of the shadows of the three views of the shell model of partitions, version "Tree", with n shells.
|
|
6
|
|
|
0, 3, 10, 21, 42, 69, 123, 189, 304, 458, 693, 998, 1474, 2067, 2927, 4056, 5613, 7595, 10335, 13782, 18411, 24276, 31944, 41583, 54152, 69762, 89758, 114668, 146181, 185083, 234051, 294126, 368992, 460669, 573906, 711865, 881506, 1087023, 1338043
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Each part is represented by a cuboid 1 X 1 X L where L is the size of the part.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
For n = 7 the shadows of the three views of the shell model of partitions version "tree" with seven shells looks like this:
. | Partitions
. |
. 1 * * * * * * 1 | 7
. 2 * * * 1 * * 2 | 4+3
. 2 * * * * 1 * 2 | 5+2
. 3 * * 1 * 2 * 3 | 3+2+2
. 1 2 * * * * * 1 2 | 6+1
. 2 3 * * 1 * * 2 3 | 3+3+1
. 2 3 * * * 1 * 2 3 | 4+2+1
. 3 4 * 1 * 2 * 3 4 | 2+2+2+1
. 3 1 * * * * 1 2 3 | 5+1+1
. 4 2 * * 1 * 2 3 4 | 3+2+1+1
. 1 4 * * * 1 2 3 4 | 4+1+1+1
. 2 5 * 1 * 2 3 4 5 | 2+2+1+1+1
. 5 1 * * 1 2 3 4 5 | 3+1+1+1+1
. 1 6 * 1 2 3 4 5 6 | 2+1+1+1+1+1
. 7 1 2 3 4 5 6 7 | 1+1+1+1+1+1+1
. ---------------------------------- |
. |
. * * * * 1 * * * * |
. * * * 1 2 * * * * |
. * 1 * * 2 1 * * * |
. * * 1 2 2 * * 1 * |
. * * * * 2 2 1 * * |
. 1 2 2 3 2 * * * * |
. 2 3 2 2 1 |
. |
.
Note that, as a variant, in this case each part is labeled with its position in the partition.
The areas of the shadows of the three views are A066186(7) = 105, A194804(7) = 59 and A194805(7) = 25, therefore the total area of the three shadows is 105+59+25 = 189, so a(7) = 189.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|