A215468 - OEIS

A215468

Sum of the 8 nearest neighbors of n in a rotated-square spiral with positive integers.

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:

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

\ /

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,

for y in range(SIZE):

for x in range(SIZE):

print '%3d' % grid[y*SIZE+x],

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