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%I #14 Dec 22 2024 10:51:23
%S 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,
%T 40,45,53,12,19,30,36,48,54,60,72,13,21,33,39,52,59,68,78,89,15,23,38,
%U 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
%N 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.
%C 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.
%H Hugo Pfoertner, <a href="/A354704/b354704.txt">Table of n, a(n) for n = 1..210</a>, rows 1..20 of triangle, flattened
%H Hugo Pfoertner, <a href="/A354704/a354704.pdf">Illustrations of the initial terms up to T(5,5)</a>.
%e The triangle begins:
%e \ h 1 2 3 4 5 6 7 8 9 10 11 12
%e w \ ----------------------------------------------------
%e 1 | 2; | | | | | | | | | | |
%e 2 | 3, 5; | | | | | | | | | |
%e 3 | 5, 8, 13; | | | | | | | | |
%e 4 | 6, 10, 15, 18; | | | | | | | |
%e 5 | 8, 12, 20, 24, 32; | | | | | | |
%e 6 | 9, 14, 23, 27, 36, 41; | | | | | |
%e 7 | 10, 17, 25, 30, 40, 45, 53; | | | | |
%e 8 | 12, 19, 30, 36, 48, 54, 60, 72; | | | |
%e 9 | 13, 21, 33, 39, 52, 59, 68, 78, 89; | | |
%e 10 | 15, 23, 38, 45, 60, 68, 75, 90, 98, 113; | |
%e 11 | 16, 25, 40, 48, 64, 72, 81, 96, 105, 120, 128; |
%e 12 | 17, 28, 43, 52, 68, 77, 88, 102, 114, 128, 137, 149
%o (PARI) \\ See links in A354702 and A355244.
%Y Cf. A293330, A354702, A354705, A354706 (diagonal), A354707, A355244.
%Y Cf. A123690 (similar problem with circular disks).
%K nonn,tabl
%O 1,1
%A _Hugo Pfoertner_, Jun 15 2022