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A343203
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Sum of x- and y-coordinate of a point moving in a triangular spiral.
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0
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0, 1, 1, -1, -3, -2, -1, 0, 1, 2, 2, 2, 2, 0, -2, -4, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 3, 3, 3, 3, 3, 1, -1, -3, -5, -7, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 2, 0, -2, -4, -6, -8, -10, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15
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OFFSET
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0,5
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LINKS
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EXAMPLE
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y
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4 | 56
| \
| \
| \
3 | 30 55
| / \ \
| / \ \
| / \ \
2 | 31 12 29 54
| / / \ \ \
| / / \ \ \
| / / \ \ \
1 | 32 13 2 11 28 53
| / / / \ \ \ \
| / / / \ \ \ \
| / / / \ \ \ \
0 | 33 14 3 0---1 10 27 52
| / / / \ \ \
| / / / \ \ \
| / / / \ \ \
-1 | 34 15 4---5---6---7---8---9 26 51
| / / \ \
| / / \ \
| / / \ \
-2 | 35 16--17--18--19--20--21--22--23--24--25 50
| / \
| / \
| / \
-3 | 36--37--38--39--40--41--42--43--44--45--46--47--48--49
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+--------------------------------------------------------
x: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Count as follows. Start at n=0 with coordinates (0,0). So first term is 0.
Next step is to move to n=1 with coordinates (1,0) resulting in sum=1. So the sequence begins 0,1,...
Next step is to move to n=2 with coordinates (0,1) resulting in sum=1. So the sequence begins 0,1,1,...
Next step is to move to n=3 with coordinates (-1,0) resulting in sum=-1. So the sequence begins 0,1,1,1,...
Next step is to move to n=4 with coordinates (-2,-1) resulting in sum=-3. So the sequence begins 0,1,1,-1,-3,...
and so on.
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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