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%I #9 Aug 12 2018 17:23:14
%S 1,2,13,3,5,6,7,8,9,10,12,32,61,33,14,4,18,19,20,21,22,23,24,25,26,27,
%T 11,31,60,98,145,99,62,34,15,17,40,41,42,43,44,45,46,47,48,49,50,51,
%U 52,53,28,30,59,97,144,200,265,201,146,100,63,35,16,39,71
%N Permutation of natural numbers arising from applying the walk of a square spiral (e.g., A214526) to the data of right triangular type-1 spiral (defined in A214230).
%e Triangular spiral (A214230) begins:
%e .
%e 56
%e | \
%e 55 57
%e | \
%e 54 29 58
%e | | \ \
%e 53 28 30 59
%e | | \ \
%e 52 27 11 31 60
%e | | | \ \ \
%e 51 26 10 12 32 61
%e | | | \ \ \
%e 50 25 9 2 13 33 62
%e | | | | \ \ \ \
%e 49 24 8 1 3 14 34 63
%e | | | \ \ \ \
%e 48 23 7---6---5---4 15 35 64
%e | | \ \ \
%e 47 22--21--20--19--18--17--16 36 65
%e | \ \
%e 46--45--44--43--42--41--40--39--38--37 66
%e \
%e 78--77--76--75--74--73--72--71--70--69--68--67
%e .
%e Square spiral (defining order in which elements are fetched) begins:
%e .
%e 49 26--27--28--29--30--31
%e | | |
%e 48 25 10--11--12--13 32
%e | | | | |
%e 47 24 9 2---3 14 33
%e | | | | | | |
%e 46 23 8 1 4 15 34
%e | | | | | |
%e 45 22 7---6---5 16 35
%e | | | |
%e 44 21--20--19--18--17 36
%e | |
%e 43--42--41--40--39--38--37
%o (Python)
%o SIZE = 33 # must be 4k+1
%o grid = [0] * (SIZE*SIZE)
%o posX = posY = SIZE//2
%o grid[posY*SIZE+posX]=1
%o n = 2
%o def walk(stepX, stepY, chkX, chkY):
%o global posX, posY, n
%o while 1:
%o posX+=stepX
%o posY+=stepY
%o grid[posY*SIZE+posX]=n
%o n+=1
%o if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o return
%o while 1:
%o walk(0, -1, 1, 1) # up
%o walk( 1, 1, -1, 0) # right-down
%o if posX==SIZE-1:
%o break
%o walk(-1, 0, 0, -1) # left
%o import sys
%o grid2 = [0] * (SIZE*SIZE)
%o posX = posY = SIZE//2
%o grid2[posY*SIZE+posX]=1
%o def walk2(stepX, stepY, chkX, chkY):
%o global posX, posY
%o while 1:
%o a = grid[posY*SIZE+posX]
%o if a==0:
%o sys.exit(1)
%o print a,
%o posX+=stepX
%o posY+=stepY
%o grid2[posY*SIZE+posX]=1
%o if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o return
%o while posX:
%o walk2(0, -1, 1, 0) # up
%o walk2(1, 0, 0, 1) # right
%o walk2(0, 1, -1, 0) # down
%o walk2(-1, 0, 0, -1) # left
%Y Cf. A090861, A214526, A214230.
%K nonn,easy
%O 1,2
%A _Alex Ratushnyak_, Sep 23 2012
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