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.

3, 7, 15, 13, 28, 53, 21, 44, 82, 127, 31, 65, 122, 190, 285, 43, 89, 166, 256, 382, 511, 57, 118, 220, 339, 506, 678, 901, 73, 150, 279, 430, 642, 860, 1142, 1447, 91, 187, 348, 536, 801, 1073, 1424, 1804, 2249, 111, 227, 421, 647, 966, 1290, 1710, 2164, 2696, 3231

Offset

2,1

Comments

T(m,n) = A332372(m,n) - A332371(m,n) + 1 (this is Euler's formula).

Links

Table of n, a(n) for n=2..56.

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,
7, 15,
13, 28, 53,
21, 44, 82, 127,
31, 65, 122, 190, 285,
43, 89, 166, 256, 382, 511,
57, 118, 220, 339, 506, 678, 901,
73, 150, 279, 430, 642, 860, 1142, 1447,
91, 187, 348, 536, 801, 1073, 1424, 1804, 2249,
...

Maple

See A332367.

Crossrefs

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

For main diagonal see A332375.

Sequence in context: A102032 A086517 A346296 * A152677 A135374 A253582

Adjacent sequences: A332371 A332372 A332373 * A332375 A332376 A332377

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 12 2020

Status

approved