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A210979 Total area of the shadows of the three views of the version "Tree" of the shell model of partitions with n shells.

%I A210979 #21 May 24 2012 09:48:31
%S A210979 0,3,8,15,27,42,69,102,155,225,327,458,652,894,1232,1669,2257,2999,
%T A210979 3996,5242,6877,8928,11564,14845,19045,24223,30756,38815,48877,61195,
%U A210979 76496,95124,118067,145930,179991,221160,271268,331538,404463,491948,597253
%N A210979 Total area of the shadows of the three views of the version "Tree" of the shell model of partitions with n shells.
%C A210979 The physical model shows each part of a partition as an object, for example; a cube of side 1 which is labeled with the size of the part. Note that on the branches of the tree each column contains parts of the same size, as a periodic structure. For the large version of this model see A210980.
%F A210979 a(n) = A006128(n) + A194803(n) + A194805(n).
%e A210979 For n = 7 the three views of the shell model of partitions version "tree" with seven shells looks like this:
%e A210979 .
%e A210979 .         A194805(7) = 25        A006128(7) = 54
%e A210979 .
%e A210979 .                        7       7
%e A210979 .                      4         4 3
%e A210979 .                    5           5 2
%e A210979 .                  3             3 2 2
%e A210979 .        6       1               6 1
%e A210979 .          3     1               3 3 1
%e A210979 .            4   1               4 2 1
%e A210979 .              2 1               2 2 2 1
%e A210979 .                1   5           5 1 1
%e A210979 .                1 3             3 2 1 1
%e A210979 .            4   1               4 1 1 1
%e A210979 .              2 1               2 2 1 1 1
%e A210979 .                1 3             3 1 1 1 1
%e A210979 .              2 1               2 1 1 1 1 1
%e A210979 .                1               1 1 1 1 1 1 1
%e A210979 -------------------------------------------------
%e A210979 .
%e A210979 .        6 3 4 2 1 3 5 4 7
%e A210979 .          3 2 2 1 2 2 3
%e A210979 .              2 1 2
%e A210979 .                1
%e A210979 .                1
%e A210979 .                1
%e A210979 .                1
%e A210979 .
%e A210979 .         A194803(7) = 23
%e A210979 .
%e A210979 The areas of the shadows of the three views are A006128(7) = 54, A194803(7) = 23 and A194805(7) = 25, therefore the total area of the three shadows is 54+23+25 = 102, so a(7) = 102.
%Y A210979 Other versions: A207380, A210970, A210980, A210990, A210991.
%Y A210979 Cf. A006128, A135010, A138121, A182703, A194803, A194805.
%K A210979 nonn
%O A210979 0,2
%A A210979 _Omar E. Pol_, Apr 28 2012