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- for n = 1, every 'e' value exists
- For a(n) functions, n = (x+1)/2 for odd, and x/2 for even.
- -------------------------------------------------------------
- (0,1), Even Xs from 2
- d : a(n) = 2*n*(n+1) from n = 1 (A046092).
- 4 times triangular numbers.
- a : a(n) = 2*n^2 from n = 1 (A001105).
- 2 times square numbers.
- -
- (1,1), Odd Xs from 1 (same as the rest odd 'e')
- d : a(n) = 2*n^2 from n = 1 (A001105).
- a : a(n) = 2*n*(n+1)+1 from n = 0 (A001844).
- Sums of two consecutive squares.
- Centered square numbers.
- -
- (2,1), Even Xs from 0 (same as the rest even 'e')
- d : a(n) = 2*n*(n+1)+1 (A001844).
- a : a(n) = 2*n^2 + 1 (A058331).
- 2 times square numbers + 1.
- -
- (3,1)
- d : a(n) = 2*n^2 + 1 (A058331).
- a : a(n) = 2*(n^2 - n + 1) (A051890).
- -
- (4,1)
- d : a(n) = 2*(n^2 - n + 1) (A051890).
- a : a(n) = 2*n^2 + 2 (A271624).
- -
- (5,1)
- d : a(n) = 2*n^2 + 2 (A271624).
- a : a(n) = 2*n^2 - 2*n + 3 (A097080).
- -
- (6,1)
- d : a(n) = 2*n^2 - 2*n + 3 (A097080).
- a : a(n) = 2*n^2 + 3 (A093328).
- -
- (7,1)
- d : a(n) = 2*n^2 + 3 (A093328).
- a : a(n) = 2*(n^2 - n + 2) (A271649).
- -
- (8,1)
- d : a(n) = 2*(n^2 - n + 2) (A271649).
- a : a(n) = 2*n^2 + 4 (A255843).
- -
- (9,1)
- d : a(n) = 2*n^2 + 4 (A255843).
- a : 2*n^2 + 2*n + 5 (A294774).
- -
- (10,1)
- d : 2*n^2 + 2*n + 5 (A294774).
- a : a(n) = 2*n^2 + 6 (A255843).
- --------------------------------------------------------------
- Odd 'e' cells can be grouped together.
- Even 'e' cells can be grouped together.
- The 'd' pattern for a certain cell is the same as the 'a' pattern for the cell before it (row wise).
- Odd 'e' cells have a common pattern for their 'd' values.
- 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.
- More generalized: If n = (x+1)/2, then:
- d = 2*n^2 + (e-1)/2 (ODD e)
- n = SQRT((d - (e-1)/2)/2) (can be used in excel if 'n = 1').
- 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.
- (NEED PROOF ON WHY DO EVEN 'e' CELLS WORK ON ODD 'e' CELLS FORMULA).
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