A323621 - OEIS

%I #12 Feb 15 2019 08:21:38

%S 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,

%T 23,19,15,12,12,15,19,23,29,24,20,17,16,17,20,24,29,35,30,25,21,20,20,

%U 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

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

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

%H Rok Cestnik, <a href="/A323621/a323621_1.gif">Visualization</a>

%o (Python)

%o N = 8

%o from math import sqrt

%o # the distance to the edge of each cell

%o edges = [[-1 for j in range(N)] for i in range(N)]

%o edges[0][0] = 0

%o for i in range(1,N):

%o     edges[i][0] = i-0.5

%o     edges[0][i] = i-0.5

%o for i in range(1,N):

%o     for j in range(1,N):

%o         edges[i][j] = sqrt((i-0.5)**2+(j-0.5)**2)

%o # the values of the distances

%o values = []

%o for i in range(N):

%o     for j in range(N):

%o         values.append(edges[i][j])

%o values = list(set(values))

%o values.sort()

%o # the cell order

%o board = [[-1 for j in range(N)] for i in range(N)]

%o count = 0

%o for v in values:

%o     for i in range(N):

%o         for j in range(N):

%o             if(edges[i][j] == v):

%o                 board[i][j] = count

%o     count += 1

%o # print out the sequence

%o for i in range(N):

%o     for j in range(i+1):

%o         print(str(board[j][i-j])+" ", end="")

%Y For the first row of the grid see A323622.

%Y For the second row of the grid see A323623.

%Y For the diagonal of the grid see A323624.

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

%Y Cf. A232499.

%K nonn

%O 0,4

%A _Rok Cestnik_, Jan 20 2019