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A160248
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Table read by antidiagonals of "less regular" truncated tetrahedron numbers built of face-centered-cubic sphere packing.
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0
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1, 6, 4, 19, 16, 10, 44, 40, 31, 20, 85, 80, 68, 52, 35, 146, 140, 125, 104, 80, 56, 231, 224, 206, 180, 149, 116, 84, 344, 336, 315, 284, 246, 204, 161, 120, 489, 480, 456, 420, 375, 324, 270, 216, 165
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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These also contain 3 existing sequences:
1: Regular octahedra (A005900) on the x-axis, which represents the increasing edge at truncation.
2: Regular tetrahedra (essentially A000292) on the y-axis, which represents the increasing remaining original edge.
3: Regular truncated tetrahedra (A005906) on the diagonal, which represents values where the newly formed edge and the remaining portion of the original tetrahedron edge are of equal length.
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REFERENCES
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Main Title: Polyhedra primer / Peter Pearce and Susan Pearce. Published/Created: New York : Van Nostrand Reinhold, c1978. Description: viii, 134 p. : ill. ; 24 cm. ISBN: 0442264968
Main Title: The book of numbers / John H. Conway, Richard K. Guy. Published/Created: New York, NY : Copernicus c1996. Description: ix, 310 p. : ill. (some col.) ; 24 cm. ISBN: 038797993X
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LINKS
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FORMULA
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v=(y^3+4*x^3+6*y^2*x+12*y*x^2-3*y^2-12*x^2-12*y*x+2*y+8*x)/6
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PROG
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(Excel) Paste the following formula into cell C3, and fill down and right to desired table size. All volumes 10, 000 and under are covered by column AA and row 41.
=((ROW()-2)^3+4*(COLUMN()-2)^3+6*(ROW()-2)^2*(COLUMN()-2)+12*(ROW()-2)*(COLUMN()-2)^2-3*(ROW()-2)^2-12*(COLUMN()-2)^2-12*(ROW()-2)*(COLUMN()-2)+2*(ROW()-2)+8*(COLUMN()-2))/6
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CROSSREFS
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KEYWORD
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AUTHOR
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Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009
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EXTENSIONS
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Improvement of the definition's precision by Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 19 2009
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STATUS
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approved
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