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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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: A005009 A135092 A245417 * A058530 A293359 A134384

Adjacent sequences:  A332368 A332369 A332370 * A332372 A332373 A332374

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 12 2020

STATUS

approved

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Last modified September 21 02:11 EDT 2020. Contains 337266 sequences. (Running on oeis4.)