A323622 The first row of the order of square grid cells touched by a circle expanding from the middle of a cell.

0, 1, 3, 6, 9, 13, 18, 23, 29, 35, 42, 48, 57, 65, 74, 84, 94, 104, 115, 127, 138, 151, 163, 177, 192, 205, 221, 235, 250, 267, 284, 301, 317, 337, 356, 376, 394, 415, 436, 456, 477, 500, 521, 546, 568, 590, 616, 640, 666, 690, 716, 745, 770, 798, 826, 855, 884, 913, 942, 973, 1003, 1033, 1066

Offset

0,3

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..62.

Rok Cestnik, Visualization

Prog

(Python)
N = 12
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):
    print(str(board[i][0])+" ", end="")

Crossrefs

For the grid read by antidiagonals see A323621.

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: A310159 A282720 A129403 * A154287 A092847 A143975

Adjacent sequences: A323619 A323620 A323621 * A323623 A323624 A323625

Keyword

nonn

Author

Rok Cestnik, Jan 20 2019

Status

approved