A214250 Sum of the eight nearest neighbors of n in a triangular "horizontal-first" spiral with positive integers.

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

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