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A210970
Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells.
10
0, 3, 9, 18, 34, 55, 91, 136, 208, 301, 439, 616, 876, 1203, 1665, 2256, 3062, 4083, 5459, 7186, 9470, 12335, 16051, 20688, 26648, 34027, 43395, 54966, 69496, 87341, 109591, 136766, 170382, 211293, 261519, 322382, 396694, 486327, 595143, 725954, 883912
OFFSET
0,2
COMMENTS
For more information see A135010 and A182703.
FORMULA
a(n) = 2*A006128(n) + A000217(n).
EXAMPLE
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:
.
. A006128(6) = 35 A006128(6) = 35
.
. 6 6
. 3 3 3 3
. 4 2 4 2
. 2 2 2 2 2 2
. 5 1 5 1
. 3 2 1 3 2 1
. 4 1 1 4 1 1
. 2 2 1 1 2 2 1 1
. 3 1 1 1 3 1 1 1
. 2 1 1 1 1 2 1 1 1 1
. 1 1 1 1 1 1 1 1 1 1 1 1
.
.
. 1 2 5 9 12 6 \
. 1 1 3 5 6 \
. 1 1 2 4 \ 6th slice of
. 1 1 2 / tetrahedron A210961
. 1 1 /
. 1 /
.
. A000217(6) = 21
.
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.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 22 2012
STATUS
approved