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).

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

Author

Hugo Pfoertner, Jan 23 2020

Keywords

• nonn
• frac

Comments

The side lengths (i,j,k) of the triangles in the list sorted by area are given in A331251, A331252, and A331253.

Examples

			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)
		

Crossrefs

Cf. A331248, A331249, A331251, A331252, A331253, A331695, A331696, A331697.