A323621 The order of square grid cells touched by a circle expanding from the middle of a cell read by antidiagonals.

0, 1, 1, 3, 2, 3, 6, 4, 4, 6, 9, 7, 5, 7, 9, 13, 10, 8, 8, 10, 13, 18, 14, 11, 10, 11, 14, 18, 23, 19, 15, 12, 12, 15, 19, 23, 29, 24, 20, 17, 16, 17, 20, 24, 29, 35, 30, 25, 21, 20, 20, 21, 25, 30, 35, 42, 36, 31, 26, 24, 22, 24, 26, 31, 36, 42, 48, 43, 37, 33, 28, 27, 27, 28, 33, 37, 43, 48, 57, 49, 44, 39, 34, 33, 32, 33, 34, 39, 44, 49, 57

Offset

0,4

Comments

Related to, but not the same as the case with the circle centered at the corner of a cell, see A232499.

Links

Table of n, a(n) for n=0..90.

Rok Cestnik, Visualization

Prog

(Python)
N = 8
from math import sqrt
# the distance to the edge of each cell
edges = [[-1 for j in range(N)] for i in range(N)]
edges[0][0] = 0
for i in range(1, N):
    edges[i][0] = i-0.5
    edges[0][i] = i-0.5
for i in range(1, N):
    for j in range(1, N):
        edges[i][j] = sqrt((i-0.5)**2+(j-0.5)**2)
# the values of the distances
values = []
for i in range(N):
    for j in range(N):
        values.append(edges[i][j])
values = list(set(values))
values.sort()
# the cell order
board = [[-1 for j in range(N)] for i in range(N)]
count = 0
for v in values:
    for i in range(N):
        for j in range(N):
            if(edges[i][j] == v):
                board[i][j] = count
    count += 1
# print out the sequence
for i in range(N):
    for j in range(i+1):
        print(str(board[j][i-j])+" ", end="")

Crossrefs

For the first row of the grid see A323622.

For the second row of the grid see A323623.

For the diagonal of the grid see A323624.

For the (2,1) diagonal of the grid see A323625.

Cf. A232499.

Sequence in context: A220075 A266593 A130459 * A144216 A127938 A131990

Adjacent sequences: A323618 A323619 A323620 * A323622 A323623 A323624

Keyword

nonn

Author

Rok Cestnik, Jan 20 2019

Status

approved