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A215468 Sum of the 8 nearest neighbors of n in a rotated-square spiral with positive integers. 5
50, 62, 72, 86, 76, 84, 122, 88, 144, 104, 166, 120, 152, 160, 144, 218, 160, 168, 248, 184, 192, 278, 208, 216, 260, 268, 240, 248, 346, 264, 272, 280, 384, 296, 304, 312, 422, 328, 336, 344, 400, 408, 368, 376, 384, 506, 400, 408, 416, 424, 552, 440, 448, 456, 464, 598 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

Spiral begins:

                     85

                     /

                    /

                  84 61-62

                  /  /    \

                 /  /      \

               83 60 41-42 63

               /  /  /    \  \

              /  /  /      \  \

            82 59 40 25-26 43 64

            /  /  /  /    \  \  \

           /  /  /  /      \  \  \

         81 58 39 24 13-14 27 44 65

         /  /  /  /  /    \  \  \  \

        /  /  /  /  /      \  \  \  \

      80 57 38 23 12  5--6 15 28 45 66

      /  /  /  /  /  /    \  \  \  \  \

     /  /  /  /  /  /      \  \  \  \  \

   79 56 37 22 11  4  1--2  7 16 29 46 67

     \  \  \  \  \  \   /  /  /  /  /  /

      \  \  \  \  \  \ /  /  /  /  /  /

      78 55 36 21 10  3  8 17 30 47 68

        \  \  \  \  \   /  /  /  /  /

         \  \  \  \  \ /  /  /  /  /

         77 54 35 20  9 18 31 48 69

           \  \  \  \   /  /  /  /

            \  \  \  \ /  /  /  /

            76 53 34 19 32 49 70

              \  \  \   /  /  /

               \  \  \ /  /  /

               75 52 33 50 71

                 \  \   /  /

                  \  \ /  /

                  74 51 72

                    \   /

                     \ /

                     73

.

The 8 nearest neighbors of 4 are 1,3,5,10,11,12,21,23, their sum is 86, so a(4)=86.

PROG

(Python)

SIZE=17  # must be odd

grid = [0] * (SIZE*SIZE)

posX = posY = SIZE//2

saveX = [0]* (SIZE*SIZE+1)

saveY = [0]* (SIZE*SIZE+1)

grid[posY*SIZE+posX]=1

saveX[1]=posX

saveY[1]=posY

posX += 1

grid[posY*SIZE+posX]=2

saveX[2]=posX

saveY[2]=posY

n = 3

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 grid[(posY+chkY)*SIZE+posX+chkX]==0:

        return

while posX!=SIZE-1:

    walk(-1,  1, -1, -1)    # down-left

    walk(-1, -1,  1, -1)    # up-left

    walk( 1, -1,  1,  0)    # up-right

    walk( 1,  0,  1,  1)    # right

    walk( 1,  1, -1,  1)    # down-right

for s in range(1, n):

    posX = saveX[s]

    posY = saveY[s]

    i, j = grid[(posY-1)*SIZE+posX-1], grid[(posY-1)*SIZE+posX+1]

    u, v = grid[(posY+1)*SIZE+posX-1], grid[(posY+1)*SIZE+posX+1]

    if i==0 or j==0 or u==0 or v==0:

        break

    k = grid[(posY-1)*SIZE+posX  ] + grid[(posY+1)*SIZE+posX  ]

    k+= grid[ posY   *SIZE+posX-1] + grid[ posY   *SIZE+posX+1]

    print i+j+u+v+k,

print

for y in range(SIZE):

    for x in range(SIZE):

        print '%3d' % grid[y*SIZE+x],

    print

CROSSREFS

Coordinates (but 0-based): A010751, A305258.

Other spiral sums: A214176, A214177, A214226, A214227, A214230, A214231, A214250, A214251, A214252.

Sequence in context: A062118 A167329 A179796 * A109552 A206263 A007692

Adjacent sequences:  A215465 A215466 A215467 * A215469 A215470 A215471

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Aug 11 2012

STATUS

approved

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Last modified August 14 17:36 EDT 2022. Contains 356122 sequences. (Running on oeis4.)