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A217011 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of right triangular type-2 spiral (defined in A214251).

%I A217011 #9 Mar 12 2025 20:08:11
%S A217011 1,5,19,6,8,9,10,2,3,4,18,41,73,42,20,7,24,25,26,27,28,11,12,13,14,15,
%T A217011 17,40,72,113,163,114,74,43,21,23,49,50,51,52,53,54,55,29,30,31,32,33,
%U A217011 34,35,16,39,71,112,162,221
%N A217011 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of right triangular type-2 spiral (defined in A214251).
%o A217011 (Python)
%o A217011 SIZE = 33       # must be 4k+1
%o A217011 grid = [0] * (SIZE*SIZE)
%o A217011 posX = posY = SIZE//2
%o A217011 grid[posY*SIZE+posX]=1
%o A217011 n = 2
%o A217011 def walk(stepX, stepY, chkX, chkY):
%o A217011   global posX, posY, n
%o A217011   while 1:
%o A217011     posX+=stepX
%o A217011     posY+=stepY
%o A217011     grid[posY*SIZE+posX]=n
%o A217011     n+=1
%o A217011     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217011         return
%o A217011 while 1:
%o A217011     walk(-1, 0,  0, -1)    # left
%o A217011     walk(0, -1,  1,  1)    # up
%o A217011     if posY==0:
%o A217011         break
%o A217011     walk( 1, 1, -1,  0)    # right-down
%o A217011 import sys
%o A217011 grid2 = [0] * (SIZE*SIZE)
%o A217011 posX = posY = SIZE//2
%o A217011 grid2[posY*SIZE+posX]=1
%o A217011 def walk2(stepX, stepY, chkX, chkY):
%o A217011   global posX, posY
%o A217011   while 1:
%o A217011     a = grid[posY*SIZE+posX]
%o A217011     if a==0:
%o A217011         sys.exit(1)
%o A217011     print(a, end=', ')
%o A217011     posX+=stepX
%o A217011     posY+=stepY
%o A217011     grid2[posY*SIZE+posX]=1
%o A217011     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217011         return
%o A217011 while 1:
%o A217011     walk2(0, -1, 1, 0)    # up
%o A217011     walk2(1, 0, 0, 1)     # right
%o A217011     walk2(0, 1, -1, 0)    # down
%o A217011     walk2(-1, 0, 0, -1)   # left
%Y A217011 Cf. A090861, A214526, A214251, A217010.
%K A217011 nonn,easy
%O A217011 1,2
%A A217011 _Alex Ratushnyak_, Sep 23 2012