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 A214230 Sum of the eight nearest neighbors of n in a right triangular type-1 spiral with positive integers. 6
 53, 88, 78, 125, 85, 84, 125, 97, 108, 143, 223, 168, 158, 169, 201, 284, 208, 183, 179, 187, 210, 281, 226, 219, 227, 235, 261, 314, 430, 339, 311, 310, 318, 326, 346, 396, 515, 403, 360, 347, 355, 363, 371, 379, 411, 509, 427, 411, 419, 427, 435, 443, 451, 486, 557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Right triangular type-1 spiral implements the sequence Up, Right-down, Left. Right triangular type-2 spiral (A214251): Left, Up, Right-down. Right triangular type-3 spiral (A214252): Right-down, Left, Up. A140064 -- rightwards from 1: 3,14,34... A064225 -- leftwards from 1: 8,24,49... A117625 -- upwards from 1: 2,12,31... A006137 -- downwards from 1: 6,20,43... A038764 -- left-down from 1: 7,22,46... A081267 -- left-up from 1: 9,26,52... A081589 -- right-up from 1: 13, 61, 145... 9*x^2/2 - 19*x/2 + 6 -- right-down from 1: 5,18,40... LINKS EXAMPLE Right triangular spiral begins: 56 55  57 54  29  58 53  28  30  59 52  27  11  31  60 51  26  10  12  32  61 50  25   9   2  13  33  62 49  24   8   1   3  14  34  63 48  23   7   6   5   4  15  35  64 47  22  21  20  19  18  17  16  36  65 46  45  44  43  42  41  40  39  38  37  66 78  77  76  75  74  73  72  71  70  69  68  67 The eight nearest neighbors of 3 are 1, 2, 13, 33, 14, 4, 5, 6. Their sum is a(3)=78. 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(0, -1,  1,  1)    # up     if posY==0:         break     walk( 1, 1, -1,  0)    # right-down     walk(-1, 0,  0, -1)    # left 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. A214251, A214252. Cf. A214226, A214231. Sequence in context: A144939 A118149 A251144 * A272367 A119289 A124282 Adjacent sequences:  A214227 A214228 A214229 * A214231 A214232 A214233 KEYWORD nonn,easy AUTHOR Alex Ratushnyak, Jul 08 2012 STATUS approved

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Last modified September 25 22:49 EDT 2020. Contains 337346 sequences. (Running on oeis4.)