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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
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
For main diagonal see A114043.
Sequence in context: A135092 A245417 A348111 * A058530 A293359 A134384
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 12 2020
STATUS
approved

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Last modified May 27 16:57 EDT 2024. Contains 372880 sequences. (Running on oeis4.)