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A358877
Triangle read by rows: T(n,k) is the number of cubes of side length k that can be placed inside a cube of side length n without overlap, 1 <= k <= n.
0
1, 8, 1, 27, 1, 1, 64, 8, 1, 1, 125, 8, 1, 1, 1, 216, 27, 8, 1, 1, 1, 343, 27, 8, 1, 1, 1, 1, 512, 64, 8, 8, 1, 1, 1, 1, 729, 64, 27, 8, 1, 1, 1, 1, 1, 1000, 125, 27, 8, 8, 1, 1, 1, 1, 1, 1331, 125, 27, 8, 8, 1, 1, 1, 1, 1, 1, 1728, 216, 64, 27, 8, 8, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
T(n,k) is a cube 1 <= k <= n.
Alternative construction: Write each column k with each cube repeated k times.
Row sums of triangle are A318742.
EXAMPLE
Triangle begins:
1;
8, 1;
27, 1, 1;
64, 8, 1, 1;
125, 8, 1, 1, 1;
216, 27, 8, 1, 1, 1;
343, 27, 8, 1, 1, 1, 1;
512, 64, 8, 8, 1, 1, 1, 1;
729, 64, 27, 8, 1, 1, 1, 1, 1;
1000, 125, 27, 8, 8, 1, 1, 1, 1, 1;
1331, 125, 27, 8, 8, 1, 1, 1, 1, 1, 1;
1728, 216, 64, 27, 8, 8, 1, 1, 1, 1, 1, 1;
...
PROG
(Python)
def T(n, k): return (n//k)**3
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Torlach Rush, Feb 17 2023
STATUS
approved