cp's OEIS Frontend

A210980 Total area of the shadows of the three views of the shell model of partitions, version "Tree", with n shells.

%I A210980 #15 May 23 2012 17:36:58
%S A210980 0,3,10,21,42,69,123,189,304,458,693,998,1474,2067,2927,4056,5613,
%T A210980 7595,10335,13782,18411,24276,31944,41583,54152,69762,89758,114668,
%U A210980 146181,185083,234051,294126,368992,460669,573906,711865,881506,1087023,1338043
%N A210980 Total area of the shadows of the three views of the shell model of partitions, version "Tree", with n shells.
%C A210980 Each part is represented by a cuboid 1 X 1 X L where L is the size of the part.
%F A210980 a(n) = A066186(n) + A194804(n) + A194805(n), n >= 1.
%e A210980 For n = 7 the shadows of the three views of the shell model of partitions version "tree" with seven shells looks like this:
%e A210980 .                                        |  Partitions
%e A210980 .    A194805(7) = 25    A066186(7) = 105 |  of 7
%e A210980 .                                        |
%e A210980 .                   1    * * * * * * 1   |  7
%e A210980 .                 2      * * * 1 * * 2   |  4+3
%e A210980 .               2        * * * * 1 * 2   |  5+2
%e A210980 .             3          * * 1 * 2 * 3   |  3+2+2
%e A210980 .   1       2            * * * * * 1 2   |  6+1
%e A210980 .     2     3            * * 1 * * 2 3   |  3+3+1
%e A210980 .       2   3            * * * 1 * 2 3   |  4+2+1
%e A210980 .         3 4            * 1 * 2 * 3 4   |  2+2+2+1
%e A210980 .           3   1        * * * * 1 2 3   |  5+1+1
%e A210980 .           4 2          * * 1 * 2 3 4   |  3+2+1+1
%e A210980 .       1   4            * * * 1 2 3 4   |  4+1+1+1
%e A210980 .         2 5            * 1 * 2 3 4 5   |  2+2+1+1+1
%e A210980 .           5 1          * * 1 2 3 4 5   |  3+1+1+1+1
%e A210980 .         1 6            * 1 2 3 4 5 6   |  2+1+1+1+1+1
%e A210980 .           7            1 2 3 4 5 6 7   |  1+1+1+1+1+1+1
%e A210980 .   ----------------------------------   |
%e A210980 .                                        |
%e A210980 .   * * * * 1 * * * *                    |
%e A210980 .   * * * 1 2 * * * *                    |
%e A210980 .   * 1 * * 2 1 * * *                    |
%e A210980 .   * * 1 2 2 * * 1 *                    |
%e A210980 .   * * * * 2 2 1 * *                    |
%e A210980 .   1 2 2 3 2 * * * *                    |
%e A210980 .           2 3 2 2 1                    |
%e A210980 .                                        |
%e A210980 .    A194804(7) = 59                     |
%e A210980 .
%e A210980 Note that, as a variant, in this case each part is labeled with its position in the partition.
%e A210980 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.
%Y A210980 Other versions: A207380, A210970, A210979, A210990, A210991.
%Y A210980 Cf. A000041, A066186, A135010, A138121, A141285, A182703, A194804, A194805, A206437.
%K A210980 nonn
%O A210980 0,2
%A A210980 _Omar E. Pol_, Apr 21 2012