A214226 Sum of the eight nearest neighbors of n in a triangular horizontal-last spiral with positive integers.

72, 80, 60, 76, 132, 100, 164, 112, 136, 200, 144, 128, 128, 136, 156, 196, 284, 220, 204, 208, 324, 224, 232, 248, 288, 384, 296, 264, 256, 264, 272, 280, 288, 296, 324, 380, 500, 404, 372, 368, 376, 384, 548, 400, 408, 416, 424, 448, 504, 632, 512, 464, 448

Offset: 1

Author

Alex Ratushnyak, Jul 07 2012

Keywords

• nonn
• easy

Examples

			Triangular spiral begins:
__ __ __ __ __ __ __ 43
__ __ __ __ __ __ 42 21 44
__ __ __ __ __ 41 20  7 22 45
__ __ __ __ 40 19  6  1  8 23 46
__ __ __ 39 18  5  4  3  2  9 24 47
__ __ 38 17 16 15 14 13 12 11 10 25 48
__ 37 36 35 34 33 32 31 30 29 28 27 26 49
64 63 62 61 60 69 58 57 56 55 54 53 52 51 50
The eight nearest neighbors of 3 are 6, 1, 8, 4, 2, 14, 13, 12; their sum is a(3)=60.
		

Crossrefs

Cf. A002061 - numbers on the central vertical axis.

Cf. A054552 - numbers on the axis starting with 1 and 2.

Cf. A214227 - sum of the four nearest neighbors.

Cf. A214250 - same sum in a triangular "horizontal-first" spiral.

Programs

Python

SIZE=27 # 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, 1, -1,  0, -1, 0)    # right+down
    walk(-1, 0,  1, -1, 0, -1)    # left
    if posX==0:
        break
    walk( 1,-1,  1, 1, 1, 1)    # right+up
for n in range(1,101):
    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=', ')