OFFSET
0,26
COMMENTS
This sequence is related to the Newton fractal, and exhibits similar rich patterns (see illustration in Links section).
LINKS
Rémy Sigrist, Colored representation of the square array for n, k <= 1000 (black, white, blue and red pixels denote, respectively, -1, 0, 1 and 2)
Rémy Sigrist, PARI program
Wikipedia, Newton fractal
Wikipedia, Newton's method
EXAMPLE
Array A(n, k) begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
----+------------------------------------------------------
0 | -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 | 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
2 | 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 1
3 | 0 0 0 0 0 2 2 1 1 1 1 1 1 1 1 1
4 | 0 0 0 0 0 0 1 2 2 1 2 1 1 1 1 1
5 | 0 0 0 0 0 0 0 0 2 2 0 1 1 1 1 1
6 | 0 0 0 0 0 0 0 0 2 1 0 2 2 1 2 2
7 | 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 0
8 | 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0
9 | 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0
10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
11 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Rémy Sigrist, Apr 22 2023
STATUS
approved