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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.

%I A323622 #13 Feb 15 2019 14:58:52
%S A323622 0,1,3,6,9,13,18,23,29,35,42,48,57,65,74,84,94,104,115,127,138,151,
%T A323622 163,177,192,205,221,235,250,267,284,301,317,337,356,376,394,415,436,
%U A323622 456,477,500,521,546,568,590,616,640,666,690,716,745,770,798,826,855,884,913,942,973,1003,1033,1066
%N A323622 The first row of the order of square grid cells touched by a circle expanding from the middle of a cell.
%C A323622 Related to, but not the same as the case with the circle centered at the corner of a cell, see A232499.
%H A323622 Rok Cestnik, <a href="/A323621/a323621_1.gif">Visualization</a>
%o A323622 (Python)
%o A323622 N = 12
%o A323622 from math import sqrt
%o A323622 # the distance to the edge of each cell
%o A323622 edges = [[-1 for j in range(N)] for i in range(N)]
%o A323622 edges[0][0] = 0
%o A323622 for i in range(1,N):
%o A323622     edges[i][0] = i-0.5
%o A323622     edges[0][i] = i-0.5
%o A323622 for i in range(1,N):
%o A323622     for j in range(1,N):
%o A323622         edges[i][j] = sqrt((i-0.5)**2+(j-0.5)**2)
%o A323622 # the values of the distances
%o A323622 values = []
%o A323622 for i in range(N):
%o A323622     for j in range(N):
%o A323622         values.append(edges[i][j])
%o A323622 values = list(set(values))
%o A323622 values.sort()
%o A323622 # the cell order
%o A323622 board = [[-1 for j in range(N)] for i in range(N)]
%o A323622 count = 0
%o A323622 for v in values:
%o A323622     for i in range(N):
%o A323622         for j in range(N):
%o A323622             if(edges[i][j] == v):
%o A323622                 board[i][j] = count
%o A323622     count += 1
%o A323622 # print out the sequence
%o A323622 for i in range(N):
%o A323622     print(str(board[i][0])+" ", end="")
%Y A323622 For the grid read by antidiagonals see A323621.
%Y A323622 For the second row of the grid see A323623.
%Y A323622 For the diagonal of the grid see A323624.
%Y A323622 For the (2,1) diagonal of the grid see A323625.
%Y A323622 Cf. A232499.
%K A323622 nonn
%O A323622 0,3
%A A323622 _Rok Cestnik_, Jan 20 2019