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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
a(n) = A066186(n) + A194804(n) + A194805(n), n >= 1.
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
. A194805(7) = 25 A066186(7) = 105 | of 7
. |
. 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 |
. |
. A194804(7) = 59 |
.
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
Other versions: A207380, A210970, A210979, A210990, A210991.
Sequence in context: A038347 A338089 A294365 * A207380 A268348 A117495
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 21 2012
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)