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A160247 Table read by antidiagonals of "less regular type 1" truncated octahedron numbers built from face-centered-cubic sphere packing. 0

%I #3 Apr 25 2016 12:08:30

%S 1,13,6,55,38,19,147,116,79,44,309,260,201,140,85,561,490,405,314,225,

%T 146,923,826,711,586,459,338,231,1415,1288,1139,976,807,640,483,344

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

%C 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.

%C 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.

%D 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

%D 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

%F 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

%o (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.

%o =(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

%K easy,nonn,tabl

%O 1,2

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

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)