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 A214251 Sum of the eight nearest neighbors of n in a right triangular type-2 spiral with positive integers. 5

%I

%S 62,64,69,125,94,111,170,118,105,116,169,132,131,151,192,284,217,201,

%T 206,220,258,353,265,234,227,235,243,269,349,285,275,283,291,299,328,

%U 387,515,412,378,374,382,390,398,421,477,608,484,435,419,427,435

%N Sum of the eight nearest neighbors of n in a right triangular type-2 spiral with positive integers.

%C Right triangular type-1 spiral (A214230): implements the sequence Up, Right-down, Left.

%C Right triangular type-2 spiral: Left, Up, Right-down.

%C Right triangular type-3 spiral (A214252): Right-down, Left, Up.

%e Right triangular type-2 spiral begins:

%e 67

%e 66 68

%e 65 37 69

%e 64 36 38 70

%e 63 35 16 39 71

%e 62 34 15 17 40 72

%e 61 33 14 4 18 41 73

%e 60 32 13 3 5 19 42 74

%e 59 31 12 2 1 6 20 43 75

%e 58 30 11 10 9 8 7 21 44 76

%e 57 29 28 27 26 25 24 23 22 45 77

%e 56 55 54 53 52 51 50 49 48 47 46 78

%e The eight nearest neighbors of 5 are 1, 2, 3, 4, 18, 41, 19, 6. Their sum is a(5)=94.

%o (Python)

%o SIZE=29 # must be odd

%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 1:

%o walk(-1, 0, 0, -1) # left

%o walk(0, -1, 1, 1) # up

%o if posY==0:

%o break

%o walk( 1, 1, -1, 0) # right-down

%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. A214252.

%K nonn,easy

%O 1,1

%A _Alex Ratushnyak_, Jul 08 2012

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Last modified September 25 16:13 EDT 2020. Contains 337344 sequences. (Running on oeis4.)