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
Offset: 1
Examples
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; | | | | | | |
6 | 9, 14, 23, 27, 36, 41; | | | | | |
7 | 10, 17, 25, 30, 40, 45, 53; | | | | |
8 | 12, 19, 30, 36, 48, 54, 60, 72; | | | |
9 | 13, 21, 33, 39, 52, 59, 68, 78, 89; | | |
10 | 15, 23, 38, 45, 60, 68, 75, 90, 98, 113; | |
11 | 16, 25, 40, 48, 64, 72, 81, 96, 105, 120, 128; |
12 | 17, 28, 43, 52, 68, 77, 88, 102, 114, 128, 137, 149
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).
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