cp's OEIS Frontend

A332369 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) = number of quadrilateral cells in the partition for m >= n >= 2.

%I A332369 #19 Feb 28 2020 13:02:55
%S A332369 3,6,9,11,18,35,18,27,52,77,27,42,81,122,191,38,57,108,159,248,321,51,
%T A332369 78,147,216,335,436,591,66,99,186,273,424,551,746,941,83,126,235,346,
%U A332369 537,698,943,1190,1503,102,153,284,415,642,829,1118,1407,1776,2097,123,186,345,504,777,1002,1349,1696,2139,2528,3047
%N A332369 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) = number of quadrilateral cells in the partition for m >= n >= 2.
%H A332369 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 A332369 N. J. A. Sloane, <a href="/A332371/a332371.pdf">Illustration for m=n=3</a>
%e A332369 Triangle begins:
%e A332369 3,
%e A332369 6, 9,
%e A332369 11, 18, 35,
%e A332369 18, 27, 52, 77,
%e A332369 27, 42, 81, 122, 191,
%e A332369 38, 57, 108, 159, 248, 321,
%e A332369 51, 78, 147, 216, 335, 436, 591,
%e A332369 66, 99, 186, 273, 424, 551, 746, 941,
%e A332369 83, 126, 235, 346, 537, 698, 943, 1190, 1503,...
%p A332369 See A332367.
%Y A332369 Cf. A332350, A332352, A331781, A332367, A332371, A332372, A332374.
%Y A332369 For main diagonal see A332370.
%K A332369 nonn,tabl
%O A332369 2,1
%A A332369 _N. J. A. Sloane_, Feb 12 2020