A160247 Table read by antidiagonals of "less regular type 1" truncated octahedron numbers built from face-centered-cubic sphere packing.

1, 13, 6, 55, 38, 19, 147, 116, 79, 44, 309, 260, 201, 140, 85, 561, 490, 405, 314, 225, 146, 923, 826, 711, 586, 459, 338, 231, 1415, 1288, 1139, 976, 807, 640, 483, 344

Offset

1,2

Comments

The sequence contains regular cuboctahedra (A005902) on the x-axis, regular octahedra (A005900) on the y-axis, and regular truncated octahedra (A005910) on the diagonal. As for the rest, they each have 6 squares of the same area, while the 8 hexagons (of another same area) have 2 side lengths which alternate.

The x-axis represents an increasing degree of truncation, while the y-axis represents an increasing quantity of units on the remaining original octahedron edge.

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..36.

Formula

v=(2*y^3+10*x^3+12*y^2x+24*Y*x^2-12*y^2-39*x^2-48*y*x+25*y+47*x-18)/3

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 Q and row 27.
=(2*(ROW()-2)^3+10*(COLUMN()-2)^3+12*(ROW()-2)^2*(COLUMN()-2)+24*(ROW()-2)*(COLUMN()-2)^2-12*(ROW()-2)^2-39*(COLUMN()-2)^2-48*(ROW()-2)*(COLUMN()-2)+25*(ROW()-2)+47*(COLUMN()-2)-18)/3

Crossrefs

Sequence in context: A220131 A268723 A300942 * A300886 A301496 A078438

Adjacent sequences: A160244 A160245 A160246 * A160248 A160249 A160250

Keyword

easy,nonn,tabl

Author

Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 19 2009

Status

approved