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%I #8 Jul 26 2012 12:59:46
%S 62,88,63,89,76,102,170,127,126,152,223,159,140,139,159,221,175,171,
%T 179,202,249,353,274,252,254,262,279,323,430,330,293,283,291,299,307,
%U 336,425,352,339,347,355,363,371,403,468,608,493,453,446,454,462,470,478,504
%N Sum of the eight nearest neighbors of n in a right triangular type-3 spiral with positive integers.
%C Right triangular type-1 spiral (A214230): implements the sequence Up, Right-down, Left.
%C Right triangular type-2 spiral (A214251): Left, Up, Right-down.
%C Right triangular type-3 spiral: Right-down, Left, Up.
%e Right triangular type-3 spiral begins:
%e 78
%e 77 46
%e 76 45 47
%e 75 44 22 48
%e 74 43 21 23 49
%e 73 42 20 7 24 50
%e 72 41 19 6 8 25 51
%e 71 40 18 5 1 9 26 52
%e 70 39 17 4 3 2 10 27 53
%e 69 38 16 15 14 13 12 11 28 54
%e 68 37 36 35 34 33 32 31 30 29 55
%e 67 66 65 64 63 62 61 60 59 58 57 56
%e The eight nearest neighbors of 5 are 1, 3, 4, 17, 18, 19, 6, 8. Their sum is a(5)=76.
%o (Python)
%o SIZE=28 # must be even
%o grid = [0] * (SIZE*SIZE)
%o saveX = [0]* (SIZE*SIZE)
%o saveY = [0]* (SIZE*SIZE)
%o saveX[1] = saveY[1] = 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 saveX[n]=posX
%o saveY[n]=posY
%o n+=1
%o if posY==0 or grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o return
%o while posY!=0:
%o walk( 1, 1, -1, 0) # right-down
%o walk(-1, 0, 0, -1) # left
%o walk(0, -1, 1, 1) # up
%o for n in range(1, 92):
%o posX = saveX[n]
%o posY = saveY[n]
%o k = grid[(posY-1)*SIZE+posX] + grid[(posY+1)*SIZE+posX]
%o k+= grid[(posY-1)*SIZE+posX-1] + grid[(posY-1)*SIZE+posX+1]
%o k+= grid[(posY+1)*SIZE+posX-1] + grid[(posY+1)*SIZE+posX+1]
%o k+= grid[posY*SIZE+posX-1] + grid[posY*SIZE+posX+1]
%o print k,
%Y Cf. A214230.
%Y Cf. A214251.
%K nonn,easy
%O 1,1
%A _Alex Ratushnyak_, Jul 08 2012
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