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A332371 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 cells in the partition for m >= n >= 2.

%I A332371 #21 Feb 13 2020 08:25:43
%S A332371 7,14,29,23,50,87,34,75,132,201,47,106,189,290,419,62,141,252,387,560,
%T A332371 749,79,182,327,504,731,980,1283,98,227,410,633,920,1235,1618,2041,
%U A332371 119,278,503,778,1133,1522,1995,2518,3107,142,333,604,935,1362,1829,2398,3027,3736,4493
%N A332371 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 cells in the partition for m >= n >= 2.
%C A332371 Equals sum of triangles A332367 and A332369.
%H A332371 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 A332371 N. J. A. Sloane, <a href="/A332371/a332371.pdf">Illustration for m=n=3</a>
%e A332371 Triangle begins:
%e A332371 7,
%e A332371 14, 29,
%e A332371 23, 50, 87,
%e A332371 34, 75, 132, 201,
%e A332371 47, 106, 189, 290, 419,
%e A332371 62, 141, 252, 387, 560, 749,
%e A332371 79, 182, 327, 504, 731, 980, 1283,
%e A332371 98, 227, 410, 633, 920, 1235, 1618, 2041,
%e A332371 119, 278, 503, 778, 1133, 1522, 1995, 2518, 3107,
%e A332371 ...
%p A332371 See A332367.
%Y A332371 Cf. A332350, A332352, A331781, A332367, A332372, A332374.
%Y A332371 For main diagonal see A114043.
%K A332371 nonn,tabl
%O A332371 2,1
%A A332371 _N. J. A. Sloane_, Feb 12 2020