cp's OEIS Frontend

A333283 Triangle read by rows: T(m,n) (m >= n >= 1) = number of edges formed by drawing the line segments connecting any two of the (m+1) X (n+1) lattice points in an m X n grid of squares and extending them to the boundary of the grid.

%I A333283 #29 Mar 23 2020 23:42:30
%S A333283 8,28,92,80,320,1028,178,716,2348,5512,372,1604,5332,12676,28552,654,
%T A333283 2834,9404,22238,49928,87540,1124,5008,16696,39496,88540,156504,
%U A333283 279100,1782,7874,26458,62818,141386,251136,447870
%N A333283 Triangle read by rows: T(m,n) (m >= n >= 1) = number of edges formed by drawing the line segments connecting any two of the (m+1) X (n+1) lattice points in an m X n grid of squares and extending them to the boundary of the grid.
%C A333283 If we only joined pairs of the 2(m+n) boundary points, we would get A331454. If we did not extend the lines to the boundary of the grid, we would get A333278. (One of the links below shows the difference between the three definitions in the case m=3, n=2.)
%C A333283 See A333282 for a large number of colored illustrations.
%H A333283 Seppo Mustonen, <a href="http://www.survo.fi/papers/GeomAccuracy.pdf">Statistical accuracy of geometric constructions</a>, 2008.
%H A333283 Seppo Mustonen, <a href="/A333282/a333282_1.pdf">Statistical accuracy of geometric constructions</a>, 2008 [Local copy]
%H A333283 Seppo Mustonen, <a href="http://www.survo.fi/papers/PointsInGrid.pdf">On lines and their intersection points in a rectangular grid of points</a>, 2009
%H A333283 Seppo Mustonen, <a href="/A018808/a018808.pdf">On lines and their intersection points in a rectangular grid of points</a>, 2009 [Local copy]
%H A333283 Seppo Mustonen, <a href="http://www.survo.fi/papers/LinesInGrid2.pdf">On lines going through a given number of points in a rectangular grid of points</a>, 2010
%H A333283 Seppo Mustonen, <a href="/A141255/a141255.pdf">On lines going through a given number of points in a rectangular grid of points</a>, 2010 [Local copy]
%H A333283 N. J. A. Sloane, <a href="/A333282/a333282.pdf">Illustration of T(3,2) = 320.</a> [Black lines correspond to A331454(3,2), black + red lines correspond to A333278(3,2), and black + red + blue lines to T(3,2)]
%H A333283 N. J. A. Sloane, <a href="/A333282/a333282_2.pdf">Illustration of T(3,3) = 1028</a> [Black lines correspond to A288187(3,3), and black + red lines to T(3,3)]
%e A333283 Triangle begins:
%e A333283 8,
%e A333283 28, 92,
%e A333283 80, 320, 1028,
%e A333283 178, 716, 2348, 5512,
%e A333283 372, 1604, 5332, 12676, 28552,
%e A333283 654, 2834, 9404, 22238, 49928, 87540,
%e A333283 1124, 5008, 16696, 39496, 88540, 156504, 279100,
%e A333283 1782, 7874, 26458, 62818, 141386, 251136, 447870, ...
%e A333283 ...
%e A333283 T(7,7) corrected Mar 19 2020
%Y A333283 Cf. A288187, A331452, A333278, A331454, A333282 (regions), A333284 (vertices). Column 1 is A331757.
%K A333283 nonn,tabl,more
%O A333283 1,1
%A A333283 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 16 2020
%E A333283 More terms and corrections from _Scott R. Shannon_, Mar 21 2020