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.

3, 6, 9, 11, 18, 35, 18, 27, 52, 77, 27, 42, 81, 122, 191, 38, 57, 108, 159, 248, 321, 51, 78, 147, 216, 335, 436, 591, 66, 99, 186, 273, 424, 551, 746, 941, 83, 126, 235, 346, 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

Offset

2,1

Links

Table of n, a(n) for n=2..67.

M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. On the minimal teaching sets of two-dimensional threshold functions. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. See Theorem 12.

N. J. A. Sloane, Illustration for m=n=3

Example

Triangle begins:
3,
6, 9,
11, 18, 35,
18, 27, 52, 77,
27, 42, 81, 122, 191,
38, 57, 108, 159, 248, 321,
51, 78, 147, 216, 335, 436, 591,
66, 99, 186, 273, 424, 551, 746, 941,
83, 126, 235, 346, 537, 698, 943, 1190, 1503,...

Maple

See A332367.

Crossrefs

Cf. A332350, A332352, A331781, A332367, A332371, A332372, A332374.

For main diagonal see A332370.

Sequence in context: A169924 A329596 A344956 * A101723 A353889 A113944

Adjacent sequences: A332366 A332367 A332368 * A332370 A332371 A332372

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 12 2020

Status

approved