A332371 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 cells in the partition for m >= n >= 2.

7, 14, 29, 23, 50, 87, 34, 75, 132, 201, 47, 106, 189, 290, 419, 62, 141, 252, 387, 560, 749, 79, 182, 327, 504, 731, 980, 1283, 98, 227, 410, 633, 920, 1235, 1618, 2041, 119, 278, 503, 778, 1133, 1522, 1995, 2518, 3107, 142, 333, 604, 935, 1362, 1829, 2398, 3027, 3736, 4493

Offset

2,1

Comments

Equals sum of triangles A332367 and A332369.

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:
7,
14, 29,
23, 50, 87,
34, 75, 132, 201,
47, 106, 189, 290, 419,
62, 141, 252, 387, 560, 749,
79, 182, 327, 504, 731, 980, 1283,
98, 227, 410, 633, 920, 1235, 1618, 2041,
119, 278, 503, 778, 1133, 1522, 1995, 2518, 3107,
...

Maple

See A332367.

Crossrefs

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

For main diagonal see A114043.

Sequence in context: A135092 A245417 A348111 * A058530 A293359 A134384

Adjacent sequences: A332368 A332369 A332370 * A332372 A332373 A332374

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 12 2020

Status

approved