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A331247
Numerator of the x-coordinate of the 3rd point (x,y) of the n-th triangle with integer sides i <= j <= k in a list sorted by increasing area, when the triangle is drawn with the shortest side from (0,0) to (0,i) and the middle side from (0,i) to (x,y). x = a(n)/A331248(n), y = sqrt(A331249(n))/A331248(n).
2
1, 1, 1, 1, 1, 9, 1, 1, 11, 1, 1, 13, 1, 3, 1, 25, 8, 1, 15, 1, 1, 29, 1, 17, 3, 1, 1, 3, 19, 1, 11, 49, 1, 2, 1, 3, 21, 10, 1, 37, 25, 1, 9, 1, 23, 55, 1, 3, 41, 1, 11, 1, 25, 2, 1, 61, 5, 81, 27, 15, 27, 1, 1, 3, 4, 1, 29, 5, 67, 1, 1, 49, 2, 89, 1, 11, 31, 3
OFFSET
1,6
COMMENTS
The side lengths (i,j,k) of the triangles in the list sorted by area are given in A331251, A331252, and A331253.
EXAMPLE
x(n) = a(n) / A331248(n),
y(n) = sqrt(A331249(n)) / A331248(n),
n i (A331251)
| | j (A331252)
| | | k (A331253)
| | | | A^2*16
| | | | | a(n) this sequence
| | | | | | A331248
| | | | | | | A331249
| | | | | | | | (x, y)
1 1 1 1 3 1 2 3 (0.5000, 0.86603)
2 1 2 2 15 1 2 15 (0.5000, 1.9365)
3 1 3 3 35 1 2 35 (0.5000, 2.9580)
4 2 2 2 48 1 1 3 (1.0000, 1.7321)
5 1 4 4 63 1 2 63 (0.5000, 3.9686)
6 2 2 3 63 9 4 63 (2.2500, 1.9843)
7 1 5 5 99 1 2 99 (0.5000, 4.9749)
8 2 3 3 128 1 1 8 (1.0000, 2.8284)
9 2 3 4 135 11 4 135 (2.7500, 2.9047)
10 1 6 6 143 1 2 143 (0.5000, 5.9791)
11 1 7 7 195 1 2 195 (0.5000, 6.9821)
12 2 4 5 231 13 4 231 (3.2500, 3.7997)
13 2 4 4 240 1 1 15 (1.0000, 3.8730)
14 3 3 3 243 3 2 27 (1.5000, 2.5981)
...
28 3 4 5 576 3 1 16 (3.0000, 4.0000)
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, Jan 23 2020
STATUS
approved