A331695 - OEIS

%I #7 Jan 25 2020 20:58:01

%S 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,

%T 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,

%U 5,51,4,1,1,9,1,25,9,49,4,9,61,35,9,41,8,19,34

%N 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).

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

%e x(n) = a(n)/A331696(n),

%e y(n) = sqrt(A331697(n))/A331696(n).

%e    n i (A316843)

%e    | | j (A316844)

%e    | | | k (A316845)

%e    | | | |  a(n) this sequence

%e    | | | |  |  A331696

%e    | | | |  |  |   A331697

%e    | | | |  |  |   |  (x,y)

%e    1 1 1 1  1  2   3  (0.5000,0.86603)

%e    2 2 2 1  1  4  15  (0.2500,0.96825)

%e    3 2 2 2  1  1   3  (1.0000,1.7321)

%e    4 3 2 2  3  2   7  (1.5000,1.3229)

%e    5 3 3 1  1  6  35  (0.16667,0.98601)

%e    6 3 3 2  2  3  32  (0.66667,1.8856)

%e    7 3 3 3  3  2  27  (1.5000,2.5981)

%e    8 4 3 2 11  8 135  (1.3750,1.4524)

%e    9 4 3 3  2  1   5  (2.0000,2.2361)

%e   10 4 4 1  1  8  63  (0.12500,0.99216)

%e   11 4 4 2  1  2  15  (0.50000,1.9365)

%e   12 4 4 3  9  8 495  (1.1250,2.7811)

%e   13 4 4 4  2  1  12  (2.0000,3.4641)

%e   14 5 3 3  5  2  11  (2.5000,1.6583)

%e   15 5 4 2 13 10 231  (1.3000,1.5199)

%e   16 5 4 3  9  5 144  (1.8000,2.4000)

%Y Cf. A316841.

%Y Sides of triangle: A316843, A316844, A316845.

%Y Cf. A331696, A331697.

%K nonn,frac

%O 1,4

%A _Hugo Pfoertner_, Jan 25 2020