A305259 - OEIS

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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

The corresponding y-coordinates of the point are given in A010751.

LINKS

Table of n, a(n) for n=1..84.

Hugo Pfoertner, Illustration of A010751(n+1) vs A305259(n).

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

Adjacent sequences: A305256 A305257 A305258 * A305260 A305261 A305262

KEYWORD

sign

AUTHOR

Hugo Pfoertner, Jun 02 2018

STATUS

approved