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%I #22 May 23 2012 17:36:32
%S 0,3,9,18,34,55,91,136,208,301,439,616,876,1203,1665,2256,3062,4083,
%T 5459,7186,9470,12335,16051,20688,26648,34027,43395,54966,69496,87341,
%U 109591,136766,170382,211293,261519,322382,396694,486327,595143,725954,883912
%N Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells.
%C For more information see A135010 and A182703.
%F a(n) = 2*A006128(n) + A000217(n).
%e For n = 6 the illustration of the three views of a three-dimensional version of the shell model of partitions with 6 shells looks like this:
%e .
%e . A006128(6) = 35 A006128(6) = 35
%e .
%e . 6 6
%e . 3 3 3 3
%e . 4 2 4 2
%e . 2 2 2 2 2 2
%e . 5 1 5 1
%e . 3 2 1 3 2 1
%e . 4 1 1 4 1 1
%e . 2 2 1 1 2 2 1 1
%e . 3 1 1 1 3 1 1 1
%e . 2 1 1 1 1 2 1 1 1 1
%e . 1 1 1 1 1 1 1 1 1 1 1 1
%e .
%e .
%e . 1 2 5 9 12 6 \
%e . 1 1 3 5 6 \
%e . 1 1 2 4 \ 6th slice of
%e . 1 1 2 / tetrahedron A210961
%e . 1 1 /
%e . 1 /
%e .
%e . A000217(6) = 21
%e .
%e The areas of the shadows of the three views are A006128(6) = 35, A006128(6) = 35 and A000217(6) = 21, therefore the total area of the three shadows is 35+35+21 = 91, so a(6) = 91.
%Y Other versions: A207380, A210979, A210980, A210990, A210991.
%Y Cf. A000217, A006128, A066186, A135010, A138121, A182703, A206437, A210952, A210961.
%K nonn
%O 0,2
%A _Omar E. Pol_, Apr 22 2012
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