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

1,2

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

Peter Pearce and Susan Pearce, Polyhedra primer, Van Nostrand Reinhold, 1979.

John H. Conway and Richard K. Guy, The book of numbers, Copernicus, 1996.

Links

Table of n, a(n) for n=1..45.

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

Prog

(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

Crossrefs

Sequence in context: A368257 A180495 A213761 * A356044 A317858 A375673

Adjacent sequences: A160245 A160246 A160247 * A160249 A160250 A160251

Keyword

easy,nonn,tabl

Author

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

Extensions

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

Status

approved