A214176 Sum of the 8 nearest neighbors of n in a spiral with positive integers.

44, 58, 72, 62, 96, 82, 120, 94, 104, 152, 120, 130, 184, 146, 144, 164, 224, 180, 176, 198, 264, 214, 208, 216, 240, 312, 256, 248, 256, 282, 360, 298, 288, 296, 304, 332, 416, 348, 336, 344, 352, 382, 472, 398, 384, 392, 400, 408, 440, 536, 456, 440

Offset: 1

Author

Alex Ratushnyak, Jul 06 2012

Keywords

• nonn
• easy

Examples

			Spiral begins:
.
  49  26--27--28--29--30--31
   |   |                   |
  48  25  10--11--12--13  32
   |   |   |           |   |
  47  24   9   2---3  14  33
   |   |   |   |   |   |   |
  46  23   8   1   4  15  34
   |   |   |       |   |   |
  45  22   7---6---5  16  35
   |   |               |   |
  44  21--20--19--18--17  36
   |                       |
  43--42--41--40--39--38--37
.
The 8 nearest neighbors of 2 are 1,3,4,8,9,10,11,12. Their sum is a(2)=58.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5202
• Rémy Sigrist, PARI program for A214176

Crossrefs

Cf. A002061, A114254, A137928, A137930, A137931.

Cf. A214177 (sum of the 4 nearest neighbors).

Programs

Mathematica

step=15; (f=Join[{12,18,24,6,32,10,40,6},Flatten@Table[{Table[0,k], s=10+2i,56+8i,s},{k,0,step},{i,2k-1,2k}]])+8Range@Length@f+24 (* Giorgos Kalogeropoulos, Sep 23 2023 *)

PARI

\\ See Links section.

Python

SIZE=11  # must be odd
grid = [0] * (SIZE*SIZE)
posX = posY = SIZE//2
grid[posY*SIZE+posX]=1
n = 2
saveX = [0]* (SIZE*SIZE+1)
saveY = [0]* (SIZE*SIZE+1)
saveX[1]=posX
saveY[1]=posY
def walk(stepX,stepY,chkX,chkY):
  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+posY==0 or grid[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while 1:
    walk(0,-1, 1, 0)    # up
    if posX+posY==0:
        break
    walk(1, 0, 0, 1)    # right
    walk(0, 1,-1, 0)    # down
    walk(-1,0, 0,-1)    # left
for n in range(1,(SIZE-2)*(SIZE-2)+1):
    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]
    print(k+grid[posY*SIZE+posX-1] + grid[posY*SIZE+posX+1], end=', ')