cp's OEIS Frontend

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).

%I A331247 #7 Jan 26 2020 07:35:59
%S A331247 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,
%T A331247 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,
%U A331247 27,15,27,1,1,3,4,1,29,5,67,1,1,49,2,89,1,11,31,3
%N 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).
%C A331247 The side lengths (i,j,k) of the triangles in the list sorted by area are given in A331251, A331252, and A331253.
%e A331247 x(n) = a(n) / A331248(n),
%e A331247 y(n) = sqrt(A331249(n)) / A331248(n),
%e A331247    n i (A331251)
%e A331247    | | j (A331252)
%e A331247    | | | k (A331253)
%e A331247    | | | |    A^2*16
%e A331247    | | | |    |  a(n) this sequence
%e A331247    | | | |    |  |  A331248
%e A331247    | | | |    |  |  |   A331249
%e A331247    | | | |    |  |  |   |  (x, y)
%e A331247    1 1 1 1    3  1  2   3  (0.5000, 0.86603)
%e A331247    2 1 2 2   15  1  2  15  (0.5000, 1.9365)
%e A331247    3 1 3 3   35  1  2  35  (0.5000, 2.9580)
%e A331247    4 2 2 2   48  1  1   3  (1.0000, 1.7321)
%e A331247    5 1 4 4   63  1  2  63  (0.5000, 3.9686)
%e A331247    6 2 2 3   63  9  4  63  (2.2500, 1.9843)
%e A331247    7 1 5 5   99  1  2  99  (0.5000, 4.9749)
%e A331247    8 2 3 3  128  1  1   8  (1.0000, 2.8284)
%e A331247    9 2 3 4  135 11  4 135  (2.7500, 2.9047)
%e A331247   10 1 6 6  143  1  2 143  (0.5000, 5.9791)
%e A331247   11 1 7 7  195  1  2 195  (0.5000, 6.9821)
%e A331247   12 2 4 5  231 13  4 231  (3.2500, 3.7997)
%e A331247   13 2 4 4  240  1  1  15  (1.0000, 3.8730)
%e A331247   14 3 3 3  243  3  2  27  (1.5000, 2.5981)
%e A331247   ...
%e A331247   28 3 4 5  576  3  1  16  (3.0000, 4.0000)
%Y A331247 Cf. A331248, A331249, A331251, A331252, A331253, A331695, A331696, A331697.
%K A331247 nonn,frac
%O A331247 1,6
%A A331247 _Hugo Pfoertner_, Jan 23 2020