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

1,1

Links

Rémy Sigrist, Table of n, a(n) for n = 1..5202

Rémy Sigrist, PARI program for A214176

Example

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.

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 *)

Prog

(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],
(PARI) See Links section.

Crossrefs

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

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

Sequence in context: A270298 A231402 A116227 * A306116 A185590 A029690

Adjacent sequences: A214173 A214174 A214175 * A214177 A214178 A214179

Keyword

nonn,easy

Author

Alex Ratushnyak, Jul 06 2012

Status

approved