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 A228747 Number T(n,k,r,c) of partitions of an n X k X r rectangular cuboid into c integer-sided cubes, considering only the list of parts; irregular triangle T(n,k,r,c), n >= k >= r >= 1, s >= 1, read by rows. 1
 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Row length = n*k*r. LINKS Christopher Hunt Gribble, Rows 1..34 flattened Christopher Hunt Gribble, C++ program EXAMPLE T(2,2,2,1) = 1 because there is 1 partition of a 2 X 2 X 2 rectangular cuboid (in this case a cube) comprising one 2 X 2 X 2 cube. T(2,2,2,8) = 1 because there is 1 partition of a 2 X 2 X 2 rectangular cuboid comprising eight 1 X 1 X 1 cubes. The irregular triangle begins: . c 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... n k r 1,1,1 1 2,1,1 0 1 2,2,1 0 0 0 1 2,2,2 1 0 0 0 0 0 0 1 3,1,1 0 0 1 3,2,1 0 0 0 0 0 1 3,2,2 0 0 0 0 1 0 0 0 0 0 0 1 3,3,1 0 0 0 0 0 0 0 0 1 3,3,2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 3,3,3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 4,1,1 0 0 0 1 4,2,1 0 0 0 0 0 0 0 1 4,2,2 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 4,3,1 0 0 0 0 0 0 0 0 0 0 0 1 4,3,2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 4,3,3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ... 4,4,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4,4,2 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ... 4,4,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 ... 4,4,4 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 ... CROSSREFS Row sums = A228202(n,k,r). Cf. A227998. Sequence in context: A185276 A375678 A266282 * A285162 A074381 A179560 Adjacent sequences: A228744 A228745 A228746 * A228748 A228749 A228750 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Sep 02 2013 STATUS approved

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Last modified September 17 05:28 EDT 2024. Contains 375985 sequences. (Running on oeis4.)