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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. Cf. A000041, A066186, A135010, A138121, A141285, A182703, A194804, A194805, A206437. Sequence in context: A027917 A038347 A294365 * A207380 A268348 A117495 Adjacent sequences:  A210977 A210978 A210979 * A210981 A210982 A210983 KEYWORD nonn AUTHOR Omar E. Pol, Apr 21 2012 STATUS approved

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Last modified May 21 03:30 EDT 2019. Contains 323434 sequences. (Running on oeis4.)