A390265 Array read by descending antidiagonals: T(n,k) is the minimal defect across all k element sets of distinct integer sided rectangles that fill an n X n square, n >= 4, k >= 2.

8, 6, 5, 4, 4, 12, 5, 6, 8, 7, 0, 5, 6, 6, 16, 0, 7, 5, 7, 10, 9, 0, 5, 5, 5, 10, 6, 20, 0, 0, 5, 7, 9, 6, 14, 11, 0, 0, 7, 6, 6, 8, 10, 9, 24, 0, 0, 0, 5, 6, 8, 9, 14, 16, 13, 0, 0, 0, 7, 7, 6, 8, 10, 8, 11, 28, 0, 0, 0, 8, 8, 7, 10, 8, 11, 16, 18, 15, 0, 0

Offset

4,1

Comments

Let the difference between the largest and smallest areas of the rectangles be called the defect. Then T(n,k) is the minimum defect when an n X n square is filled with k element sets of distinct integer sided rectangles.

Links

Table of n, a(n) for n=4..83.

Example

Array begins:
  n/k |  2     3     4     5 ...
  ----+-------------------------
   4  |  8     6     4     5 ...
   5  |  5     4     6     5 ...
   6  | 12     8     6     5 ...
   7  |  7     6     7     5 ...
   8  | 16    10    10     9 ...
   9  |  9     6     6     8 ...
  10  | 20    14    10     9 ...
  11  | 11     9    14    10 ...
  12  | 24    16     8    11 ...
  13  | 13    11    16    13 ...
  ...

Crossrefs

Cf. A296070 (k=2), A390007 (k=3), A388295 (k=4), A390168 (k=5).

Sequence in context: A061360 A353962 A120818 * A125579 A202258 A367409

Adjacent sequences: A390262 A390263 A390264 * A390266 A390267 A390268

Keyword

nonn,tabl

Author

Janaka Rodrigo, Oct 30 2025

Extensions

More terms from Sean A. Irvine, Nov 04 2025

Status

approved