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

Author

Hugo Pfoertner, Jun 15 2022

Keywords

• nonn
• tabl

Comments

See A354707 for an interpretation of the diagonal terms.

Examples

			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
		

Links

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

Crossrefs

Cf. A354707 (diagonal).

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