A160248 Table read by antidiagonals of "less regular" truncated tetrahedron numbers built of face-centered-cubic sphere packing.

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

Offset: 1

Author

Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009

Keywords

• easy
• nonn
• tabl

Comments

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.

References

• 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

Programs

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

Formula

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

Extensions

Improvement of the definition's precision by Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 19 2009