A214251 Sum of the eight nearest neighbors of n in a right triangular type-2 spiral with positive integers.

62, 64, 69, 125, 94, 111, 170, 118, 105, 116, 169, 132, 131, 151, 192, 284, 217, 201, 206, 220, 258, 353, 265, 234, 227, 235, 243, 269, 349, 285, 275, 283, 291, 299, 328, 387, 515, 412, 378, 374, 382, 390, 398, 421, 477, 608, 484, 435, 419, 427, 435

Offset: 1

Author

Alex Ratushnyak, Jul 08 2012

Keywords

• nonn
• easy

Comments

Right triangular type-1 spiral (A214230): implements the sequence Up, Right-down, Left.

Right triangular type-2 spiral: Left, Up, Right-down.

Right triangular type-3 spiral (A214252): Right-down, Left, Up.

Examples

			Right triangular type-2 spiral begins:
67
66  68
65  37  69
64  36  38  70
63  35  16  39  71
62  34  15  17  40  72
61  33  14   4  18  41  73
60  32  13   3   5  19  42  74
59  31  12   2   1   6  20  43  75
58  30  11  10   9   8   7  21  44  76
57  29  28  27  26  25  24  23  22  45  77
56  55  54  53  52  51  50  49  48  47  46  78
The eight nearest neighbors of 5 are 1, 2, 3, 4, 18, 41, 19, 6. Their sum is a(5)=94.
		

Crossrefs

Cf. A214230.

Cf. A214252.

Programs

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):
  global posX, posY, n
  while 1:
    posX+=stepX
    posY+=stepY
    grid[posY*SIZE+posX]=n
    saveX[n]=posX
    saveY[n]=posY
    n+=1
    if posY==0 or grid[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while 1:
    walk(-1, 0,  0, -1)    # left
    walk(0, -1,  1,  1)    # up
    if posY==0:
        break
    walk( 1, 1, -1,  0)    # right-down
for n in range(1, 92):
    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=', ')