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%I #3 Apr 25 2016 12:08:33
%S 1,6,4,19,16,10,44,40,31,20,85,80,68,52,35,146,140,125,104,80,56,231,
%T 224,206,180,149,116,84,344,336,315,284,246,204,161,120,489,480,456,
%U 420,375,324,270,216,165
%N Table read by antidiagonals of "less regular" truncated tetrahedron numbers built of face-centered-cubic sphere packing.
%C These also contain 3 existing sequences:
%C 1: Regular octahedra (A005900) on the x-axis, which represents the increasing edge at truncation.
%C 2: Regular tetrahedra (essentially A000292) on the y-axis, which represents the increasing remaining original edge.
%C 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.
%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=(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
%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 AA and row 41.
%o =((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
%K easy,nonn,tabl
%O 1,2
%A Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009
%E Improvement of the definition's precision by Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 19 2009
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