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A210970
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Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells.
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10
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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
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listen;
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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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:
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. 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
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. 1 2 5 9 12 6 \
. 1 1 3 5 6 \
. 1 1 2 4 \ 6th slice of
. 1 1 /
. 1 /
.
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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