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A214226 Sum of the eight nearest neighbors of n in a triangular horizontal-last spiral with positive integers. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

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.

PROG

(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,

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.

Sequence in context: A138691 A039670 A065147 * A043187 A039364 A043967

Adjacent sequences:  A214223 A214224 A214225 * A214227 A214228 A214229

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Jul 07 2012

STATUS

approved

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Last modified September 22 07:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)