A214250 Sum of the eight nearest neighbors of n in a triangular "horizontal-first" spiral with positive integers.

56, 80, 108, 84, 132, 92, 84, 96, 128, 200, 152, 144, 236, 160, 172, 204, 284, 212, 188, 184, 192, 200, 208, 232, 280, 384, 304, 280, 280, 288, 428, 304, 312, 320, 340, 388, 500, 396, 356, 344, 352, 360, 368, 376, 384, 392, 400, 432, 496, 632, 520, 480, 472, 480

Offset: 1

Author

Alex Ratushnyak, Jul 08 2012

Keywords

• nonn
• easy

Examples

			Spiral begins:
__ __ __ __ __ __ __ 57
__ __ __ __ __ __ 56 31 58
__ __ __ __ __ 55 30 13 32 59
__ __ __ __ 54 29 12  3 14 33 60
__ __ __ 53 28 11  2  1  4 15 34 61
__ __ 52 27 10  9  8  7  6  5 16 35 62
__ 51 26 25 24 23 22 21 20 19 18 17 36 63
50 49 48 47 46 45 44 43 42 41 40 39 38 37 64
The eight nearest neighbors of 4 are: 1, 3, 14, 33, 15, 5, 6, 7. Their sum is a(4)=84.
		

Crossrefs

Cf. A214226 - same sum in a triangular "horizontal-last" spiral.

Programs

Python

SIZE=29  # must be odd
grid = [0] * (SIZE*SIZE)
saveX = [0]* (SIZE*SIZE)
saveY = [0]* (SIZE*SIZE)
saveX[1] = saveY[1] = posX = posY = SIZE//2
grid[posY*SIZE+posX]=1
n = 2
def walk(stepX,stepY,chkX,chkY,chkX2,chkY2):
  global posX, posY, n
  while 1:
    posX+=stepX
    posY+=stepY
    grid[posY*SIZE+posX]=n
    saveX[n]=posX
    saveY[n]=posY
    n+=1
    if posX==0 or grid[(posY+chkY)*SIZE+posX+chkX]+grid[(posY+chkY2)*SIZE+posX+chkX2]==0:
        return
while 1:
    walk(-1, 0,  1, -1, 0, -1)   # left
    if posX==0:
        break
    walk( 1,-1,  1, 1,  1, 1)    # right+up
    walk( 1, 1, -1,  0, -1, 0)   # right+down
for n in range(1,122):
    posX = saveX[n]
    posY = saveY[n]
    k = grid[(posY-1)*SIZE+posX] + grid[(posY+1)*SIZE+posX]
    k+= grid[(posY-1)*SIZE+posX-1] + grid[(posY-1)*SIZE+posX+1]
    k+= grid[(posY+1)*SIZE+posX-1] + grid[(posY+1)*SIZE+posX+1]
    k+= grid[posY*SIZE+posX-1] + grid[posY*SIZE+posX+1]
    print(k, end=' ')