A214252 Sum of the eight nearest neighbors of n in a right triangular type-3 spiral with positive integers.

62, 88, 63, 89, 76, 102, 170, 127, 126, 152, 223, 159, 140, 139, 159, 221, 175, 171, 179, 202, 249, 353, 274, 252, 254, 262, 279, 323, 430, 330, 293, 283, 291, 299, 307, 336, 425, 352, 339, 347, 355, 363, 371, 403, 468, 608, 493, 453, 446, 454, 462, 470, 478, 504

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 (A214251): Left, Up, Right-down.

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

Examples

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

Crossrefs

Cf. A214230.

Cf. A214251.

Programs

Python

SIZE=28  # must be even
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 posY!=0:
    walk( 1, 1, -1,  0)    # right-down
    walk(-1, 0,  0, -1)    # left
    walk(0, -1,  1,  1)    # up
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=' ')