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