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A363609
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Minimum sum of the visible pips on a polycube made from n dice.
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1
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21, 30, 40, 40, 51, 52, 54, 48, 60, 62, 65, 60, 72, 74, 77, 72, 78, 74, 86, 84, 91, 88, 92, 88, 95, 93, 90, 102, 105, 102, 106, 104, 107, 110, 109, 106, 118, 120, 121, 120, 125, 123, 126, 125, 122, 128, 127, 124, 136, 138, 139, 140, 141, 138, 145, 144, 143
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OFFSET
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1,1
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COMMENTS
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This sequence is calculated using standard six-sided dice of the same chirality. Opposite sides sum to seven.
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LINKS
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FORMULA
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Conjecture: a(k^3) = 6*(k+2)*k for k > 1.
a(i*j*k) <= 48 + 2*((i-2)*(j-2) + (i-2)*(k-2) + (j-2)*(k-2)) + 12*(i+j+k-6), for i, j, k > 1. - Michael S. Branicky, Jun 15 2023
lb(n) = Sum_{i=1..A193416(n)} S(i, n),
ub(n) = Sum_{i=1..A193416(n)} S(6*n+1-i, n), and
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EXAMPLE
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For n = 2, two dice are conjoined to hide both their 6-pip faces, so a(2) = 30.
For n = 4, four dice are arranged in a 2 X 2 square such that no 5-pip or 6-pip faces are visible. When the dice can form a cube, such as n = 8, only 1-, 2- and 3-pip faces will be visible.
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PROG
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(Python) # see linked program
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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