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A332374 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 vertices in the partition for m >= n >= 2.

%I A332374 #19 Feb 13 2020 08:29:09
%S A332374 3,7,15,13,28,53,21,44,82,127,31,65,122,190,285,43,89,166,256,382,511,
%T A332374 57,118,220,339,506,678,901,73,150,279,430,642,860,1142,1447,91,187,
%U A332374 348,536,801,1073,1424,1804,2249,111,227,421,647,966,1290,1710,2164,2696,3231
%N A332374 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 vertices in the partition for m >= n >= 2.
%C A332374 T(m,n) = A332372(m,n) - A332371(m,n) + 1 (this is Euler's formula).
%H A332374 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 A332374 N. J. A. Sloane, <a href="/A332371/a332371.pdf">Illustration for m=n=3</a>
%e A332374 Triangle begins:
%e A332374 3,
%e A332374 7, 15,
%e A332374 13, 28, 53,
%e A332374 21, 44, 82, 127,
%e A332374 31, 65, 122, 190, 285,
%e A332374 43, 89, 166, 256, 382, 511,
%e A332374 57, 118, 220, 339, 506, 678, 901,
%e A332374 73, 150, 279, 430, 642, 860, 1142, 1447,
%e A332374 91, 187, 348, 536, 801, 1073, 1424, 1804, 2249,
%e A332374 ...
%p A332374 See A332367.
%Y A332374 Cf. A332350, A332352, A331781, A332367, A332371, A332372.
%Y A332374 For main diagonal see A332375.
%K A332374 nonn,tabl
%O A332374 2,1
%A A332374 _N. J. A. Sloane_, Feb 12 2020