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A332372 Consider a partition of the plane (a_1,a_2) in R X R by the lines a_1*x_1 + a_2*x_2 = 1 for 0 <= x_1 <= m-1, 1 <= x_2 <= 1-1. The cells are (generalized) triangles and quadrilaterals. Triangle read by rows: T(m,n) = total number of edges in the partition for m >= n >= 2.

%I A332372 #17 Feb 13 2020 08:28:44
%S A332372 9,20,43,35,77,139,54,118,213,327,77,170,310,479,703,104,229,417,642,
%T A332372 941,1259,135,299,546,842,1236,1657,2183,170,376,688,1062,1561,2094,
%U A332372 2759,3487,209,464,850,1313,1933,2594,3418,4321,5355,252,559,1024,1581,2327,3118,4107,5190,6431,7723
%N A332372 Consider a partition of the plane (a_1,a_2) in R X R by the lines a_1*x_1 + a_2*x_2 = 1 for 0 <= x_1 <= m-1, 1 <= x_2 <= 1-1. The cells are (generalized) triangles and quadrilaterals. Triangle read by rows: T(m,n) = total number of edges in the partition for m >= n >= 2.
%H A332372 M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. <a href="https://doi.org/10.1137/140978090">On the minimal teaching sets of two-dimensional threshold functions</a>. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. See Theorem 12.
%H A332372 N. J. A. Sloane, <a href="/A332371/a332371.pdf">Illustration for m=n=3</a>
%e A332372 Triangle begins:
%e A332372 9,
%e A332372 20, 43,
%e A332372 35, 77, 139,
%e A332372 54, 118, 213, 327,
%e A332372 77, 170, 310, 479, 703,
%e A332372 104, 229, 417, 642, 941, 1259,
%e A332372 135, 299, 546, 842, 1236, 1657, 2183,
%e A332372 170, 376, 688, 1062, 1561, 2094, 2759, 3487,
%e A332372 209, 464, 850, 1313, 1933, 2594, 3418, 4321, 5355,
%e A332372 ...
%p A332372 See A332367.
%Y A332372 Cf. A332350, A332352, A331781, A332367, A332371, A332374.
%Y A332372 For main diagonal see A332373.
%K A332372 nonn,tabl
%O A332372 2,1
%A A332372 _N. J. A. Sloane_, Feb 12 2020