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A214176 Sum of the 8 nearest neighbors of n in a spiral with positive integers. 8
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)