A214226 Sum of the eight nearest neighbors of n in a triangular horizontal-last spiral with positive integers.

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

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, end=', ')

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