A354704 - OEIS

A354704

T(w,h) is a lower bound for the maximum number of grid points in a square grid covered by an arbitrarily positioned and rotated rectangle of width w and height h, excluding the trivial case of an axis-parallel unshifted cover, where T(w,h) is a triangle read by rows.

2, 3, 5, 5, 8, 13, 6, 10, 15, 18, 8, 12, 20, 24, 32, 9, 14, 23, 27, 36, 41, 10, 17, 25, 30, 40, 45, 53, 12, 19, 30, 36, 48, 54, 60, 72, 13, 21, 33, 39, 52, 59, 68, 78, 89, 15, 23, 38, 45, 60, 68, 75, 90, 98, 113, 16, 25, 40, 48, 64, 72, 81, 96, 105, 120, 128, 17, 28, 43, 52, 68, 77, 88, 102, 114, 128, 137, 149

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Grid points must lie strictly within the covering rectangle, i.e., grid points on the perimeter of the rectangle are not allowed. See A354702 for more information.

LINKS

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

Hugo Pfoertner, Illustrations of the initial terms up to T(5,5).

EXAMPLE

The triangle begins:

\ h 1 2 3 4 5 6 7 8 9 10 11 12

w \ ----------------------------------------------------

1 | 2; | | | | | | | | | | |

2 | 3, 5; | | | | | | | | | |

3 | 5, 8, 13; | | | | | | | | |

4 | 6, 10, 15, 18; | | | | | | | |

5 | 8, 12, 20, 24, 32; | | | | | | |