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

1,1

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.

Links

Table of n, a(n) for n=1..51.

Example

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.

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):
  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,

Crossrefs

Cf. A214230.

Cf. A214252.

Sequence in context: A076764 A367090 A345496 * A031058 A084801 A095577

Adjacent sequences: A214248 A214249 A214250 * A214252 A214253 A214254

Keyword

nonn,easy

Author

Alex Ratushnyak, Jul 08 2012

Status

approved