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A305259
x-coordinates of a point moving counterclockwise on concentric squares of grid points rotated by Pi/4 with side length m*sqrt(2), m=1,2,..., with jump to next square on the positive x-axis.
1
1, 0, -1, 0, 2, 1, 0, -1, -2, -1, 0, 1, 3, 2, 1, 0, -1, -2, -3, -2, -1, 0, 1, 2, 4, 3, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, 0, 1, 2, 3, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
OFFSET
1,5
COMMENTS
The corresponding y-coordinates of the point are given in A010751.
EXAMPLE
y ^
| |
3 | 16 28
| / | \ \
| / | \ \
| / | \ \
2 | 17 7 15 27
| / / | \ \ \
| / / | \ \ \
| / / | \ \ \
1 | 18 8 2 6 14 26
| / / / | \ \ \ \
| / / / | \ \ \ \
| / / / | \ \ \ \
0 +-19------9------3------+------1------5-----13-----25->
| \ \ \ | --------/ / /
| \ \ \ | / ---------- /
| \ \ \ | / / ----------
-1 | 20 10 4 12 24
| \ \ | / /
| \ \ | / /
| \ \ | / /
-2 | 21 11 23
| \ | /
| \ | /
| \ | /
-3 | 22
| |
+-----------------------+--------------------------->
-3 -2 -1 0 1 2 3 x
PROG
(PARI) for(m=1, 6, vert=[m, 0, -m, 0, m]; for(k=1, 4, v=vert[k]; w=vert[k+1]; s=sign(w-v); forstep(j=v, w-s, s, print1(j, ", ")))) \\ Hugo Pfoertner, Jun 02 2018
CROSSREFS
Cf. A001844 (jump to next square), A010751 (y-coordinates), A304587.
Sequence in context: A284313 A169975 A168316 * A029370 A369572 A376648
KEYWORD
sign
AUTHOR
Hugo Pfoertner, Jun 02 2018
STATUS
approved