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

1,4

Comments

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

Links

Table of n, a(n) for n=1..78.

Example

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.

Sequence in context: A354092 A262218 A362940 * A245538 A080890 A251621

Adjacent sequences: A331692 A331693 A331694 * A331696 A331697 A331698

Keyword

nonn,frac

Author

Hugo Pfoertner, Jan 25 2020

Status

approved