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A214250 Sum of the eight nearest neighbors of n in a triangular "horizontal-first" spiral with positive integers. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

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.

PROG

(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,

CROSSREFS

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

Sequence in context: A039335 A043938 A328165 * A286981 A254369 A234927

Adjacent sequences:  A214247 A214248 A214249 * A214251 A214252 A214253

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Jul 08 2012

STATUS

approved

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Last modified July 12 16:03 EDT 2020. Contains 335665 sequences. (Running on oeis4.)