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A323622
The first row of the order of square grid cells touched by a circle expanding from the middle of a cell.
4
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.
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
KEYWORD
nonn
AUTHOR
Rok Cestnik, Jan 20 2019
STATUS
approved