A354705 T(w,h) = (w+1)*(h+1) - A354704(w,h) is an upper bound for the deficit in the number of grid points covered by an optimally positioned and rotated cover compared to the excluded singular case of an axis-parallel, unshifted cover, where T(w,h) and A354704 are triangles read by rows.

2, 3, 4, 3, 4, 3, 4, 5, 5, 7, 4, 6, 4, 6, 4, 5, 7, 5, 8, 6, 8, 6, 7, 7, 10, 8, 11, 11, 6, 8, 6, 9, 6, 9, 12, 9, 7, 9, 7, 11, 8, 11, 12, 12, 11, 7, 10, 6, 10, 6, 9, 13, 9, 12, 8, 8, 11, 8, 12, 8, 12, 15, 12, 15, 12, 16, 9, 11, 9, 13, 10, 14, 16, 15, 16, 15, 19, 20

Offset

1,1

Comments

See A354707 for an interpretation of the diagonal terms.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..210, rows 1..20 of triangle, flattened

Example

The triangle begins:
    \ h 1   2  3   4   5   6   7   8   9  10  11  12
   w \ ---------------------------------------------
   1 |  2;  |  |   |   |   |   |   |   |   |   |   |
   2 |  3,  4; |   |   |   |   |   |   |   |   |   |
   3 |  3,  4, 3;  |   |   |   |   |   |   |   |   |
   4 |  4,  5, 5,  7;  |   |   |   |   |   |   |   |
   5 |  4,  6, 4,  6,  4;  |   |   |   |   |   |   |
   6 |  5,  7, 5,  8,  6,  8;  |   |   |   |   |   |
   7 |  6,  7, 7, 10,  8, 11, 11;  |   |   |   |   |
   8 |  6,  8, 6,  9,  6,  9, 12,  9;  |   |   |   |
   9 |  7,  9, 7, 11,  8, 11, 12, 12, 11;  |   |   |
  10 |  7, 10, 6, 10,  6,  9, 13,  9, 12,  8;  |   |
  11 |  8, 11, 8, 12,  8, 12, 15, 12, 15, 12, 16;  |
  12 |  9, 11, 9, 13, 10, 14, 16, 15, 16, 15, 19, 20

Crossrefs

Cf. A354707 (diagonal).

Cf. A354702, A354703 (similar, but for minimizing the number of covered points), A354704.

Sequence in context: A323242 A099034 A165576 * A331730 A304730 A323374

Adjacent sequences: A354702 A354703 A354704 * A354706 A354707 A354708

Keyword

nonn,tabl

Author

Hugo Pfoertner, Jun 15 2022

Status

approved