A331695 Numerator of the x-coordinate of the 3rd point (x,y) of the n-th triangle with integer sides in the list given by A316841, when the triangle is drawn with the longest side from (0,0) to (0,A316843(n)) and the middle side A316844(n) from (0,A316843(n)) to (x,y). x = a(n)/A331696(n), y = sqrt(A331697(n))/A331696(n).

1, 1, 1, 3, 1, 2, 3, 11, 2, 1, 1, 9, 2, 5, 13, 9, 5, 1, 2, 9, 8, 5, 29, 3, 5, 5, 9, 3, 1, 1, 3, 4, 25, 3, 7, 33, 20, 7, 17, 11, 29, 19, 7, 1, 2, 9, 8, 25, 18, 7, 55, 4, 37, 11, 53, 4, 19, 3, 31, 5, 51, 4, 1, 1, 9, 1, 25, 9, 49, 4, 9, 61, 35, 9, 41, 8, 19, 34

Offset: 1

Author

Hugo Pfoertner, Jan 25 2020

Keywords

• nonn
• frac

Comments

The shortest side of the triangle has length A316845(n), i.e., x^2 + y^2 = A316845(n)^2.

Examples

			x(n) = a(n)/A331696(n),
y(n) = sqrt(A331697(n))/A331696(n).
   n i (A316843)
   | | j (A316844)
   | | | k (A316845)
   | | | |  a(n) this sequence
   | | | |  |  A331696
   | | | |  |  |   A331697
   | | | |  |  |   |  (x,y)
   1 1 1 1  1  2   3  (0.5000,0.86603)
   2 2 2 1  1  4  15  (0.2500,0.96825)
   3 2 2 2  1  1   3  (1.0000,1.7321)
   4 3 2 2  3  2   7  (1.5000,1.3229)
   5 3 3 1  1  6  35  (0.16667,0.98601)
   6 3 3 2  2  3  32  (0.66667,1.8856)
   7 3 3 3  3  2  27  (1.5000,2.5981)
   8 4 3 2 11  8 135  (1.3750,1.4524)
   9 4 3 3  2  1   5  (2.0000,2.2361)
  10 4 4 1  1  8  63  (0.12500,0.99216)
  11 4 4 2  1  2  15  (0.50000,1.9365)
  12 4 4 3  9  8 495  (1.1250,2.7811)
  13 4 4 4  2  1  12  (2.0000,3.4641)
  14 5 3 3  5  2  11  (2.5000,1.6583)
  15 5 4 2 13 10 231  (1.3000,1.5199)
  16 5 4 3  9  5 144  (1.8000,2.4000)
		

Crossrefs

Cf. A316841.

Sides of triangle: A316843, A316844, A316845.

Cf. A331696, A331697.