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  1. for n = 1, every 'e' value exists
  2.  
  3. For a(n) functions, n = (x+1)/2 for odd, and x/2 for even.
  4. -------------------------------------------------------------
  5.  
  6. (0,1), Even Xs from 2
  7. d : a(n) = 2*n*(n+1) from n = 1 (A046092).
  8. 4 times triangular numbers.
  9.  
  10. a : a(n) = 2*n^2 from n = 1 (A001105).
  11. 2 times square numbers.
  12.  
  13. -
  14.  
  15. (1,1), Odd Xs from 1 (same as the rest odd 'e')
  16. d : a(n) = 2*n^2 from n = 1 (A001105).
  17.  
  18. a : a(n) = 2*n*(n+1)+1 from n = 0 (A001844).
  19. Sums of two consecutive squares.
  20. Centered square numbers.
  21.  
  22. -
  23.  
  24. (2,1), Even Xs from 0 (same as the rest even 'e')
  25. d : a(n) = 2*n*(n+1)+1 (A001844).
  26.  
  27. a : a(n) = 2*n^2 + 1 (A058331).
  28. 2 times square numbers + 1.
  29.  
  30. -
  31.  
  32. (3,1)
  33. d : a(n) = 2*n^2 + 1 (A058331).
  34.  
  35. a : a(n) = 2*(n^2 - n + 1) (A051890).
  36.  
  37. -
  38.  
  39. (4,1)
  40. d : a(n) = 2*(n^2 - n + 1) (A051890).
  41.  
  42. a : a(n) = 2*n^2 + 2 (A271624).
  43.  
  44. -
  45.  
  46. (5,1)
  47. d : a(n) = 2*n^2 + 2 (A271624).
  48.  
  49. a : a(n) = 2*n^2 - 2*n + 3 (A097080).
  50.  
  51. -
  52.  
  53. (6,1)
  54. d : a(n) = 2*n^2 - 2*n + 3 (A097080).
  55.  
  56. a : a(n) = 2*n^2 + 3 (A093328).
  57.  
  58. -
  59.  
  60. (7,1)
  61. d : a(n) = 2*n^2 + 3 (A093328).
  62.  
  63. a : a(n) = 2*(n^2 - n + 2) (A271649).
  64.  
  65. -
  66.  
  67. (8,1)
  68. d : a(n) = 2*(n^2 - n + 2) (A271649).
  69.  
  70. a : a(n) = 2*n^2 + 4 (A255843).
  71.  
  72. -
  73.  
  74. (9,1)
  75. d : a(n) = 2*n^2 + 4 (A255843).
  76.  
  77. a : 2*n^2 + 2*n + 5 (A294774).
  78.  
  79. -
  80.  
  81. (10,1)
  82. d : 2*n^2 + 2*n + 5 (A294774).
  83.  
  84. a : a(n) = 2*n^2 + 6 (A255843).
  85. --------------------------------------------------------------
  86. Odd 'e' cells can be grouped together.
  87.  
  88. Even 'e' cells can be grouped together.
  89.  
  90. The 'd' pattern for a certain cell is the same as the 'a' pattern for the cell before it (row wise).
  91.  
  92.  
  93. Odd 'e' cells have a common pattern for their 'd' values.
  94.  
  95. let n = (x+1)/2 for odd, and x/2 for even. this "n" is the series "n" and NOT the same "n" used for our map legend (e:n:d:x:a:b) as we know here n is always 1.
  96.  
  97. More generalized: If n = (x+1)/2, then:
  98.  
  99. d = 2*n^2 + (e-1)/2 (ODD e)
  100.  
  101. n = SQRT((d - (e-1)/2)/2) (can be used in excel if 'n = 1').
  102.  
  103. Somehow, using the same formula has given us correct X values and correct A and B values for even 'e' values, so we can generalize the given formula above for all 'e' values in row 1.
  104.  
  105. (NEED PROOF ON WHY DO EVEN 'e' CELLS WORK ON ODD 'e' CELLS FORMULA).
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