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.

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.

Links

Table of n, a(n) for n=1..78.

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

Cf. A000578, A318742, A360610.

Sequence in context: A138505 A002173 A050458 * A125166 A211785 A075151

Adjacent sequences: A358874 A358875 A358876 * A358878 A358879 A358880

Keyword

nonn,tabl

Author

Torlach Rush, Feb 17 2023

Status

approved