A332372 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 edges in the partition for m >= n >= 2.

9, 20, 43, 35, 77, 139, 54, 118, 213, 327, 77, 170, 310, 479, 703, 104, 229, 417, 642, 941, 1259, 135, 299, 546, 842, 1236, 1657, 2183, 170, 376, 688, 1062, 1561, 2094, 2759, 3487, 209, 464, 850, 1313, 1933, 2594, 3418, 4321, 5355, 252, 559, 1024, 1581, 2327, 3118, 4107, 5190, 6431, 7723

Offset

2,1

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:
9,
20, 43,
35, 77, 139,
54, 118, 213, 327,
77, 170, 310, 479, 703,
104, 229, 417, 642, 941, 1259,
135, 299, 546, 842, 1236, 1657, 2183,
170, 376, 688, 1062, 1561, 2094, 2759, 3487,
209, 464, 850, 1313, 1933, 2594, 3418, 4321, 5355,
...

Maple

See A332367.

Crossrefs

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

For main diagonal see A332373.

Sequence in context: A249044 A109805 A345727 * A377002 A344818 A341529

Adjacent sequences: A332369 A332370 A332371 * A332373 A332374 A332375

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 12 2020

Status

approved