Triangular table in which the n-th row has the n numbers that are the smaller of a pair of numbers x and y such that x^2 - y^2 = A094191(n).

1, 1, 7, 2, 6, 22, 2, 5, 10, 23, 2, 8, 13, 22, 47, 4, 7, 11, 17, 28, 59, 7, 10, 18, 32, 45, 70, 143, 2, 7, 14, 19, 26, 37, 58, 119, 3, 8, 11, 24, 31, 41, 57, 88, 179, 1, 8, 14, 22, 34, 43, 56, 77, 118, 239, 16, 64, 104, 176, 244, 376, 506, 764, 1021, 1534, 3071

1

Note that A094191(43) is wrong as of today. We used the correct value, which is 9663676416.

T. D. Noe, Plot of 50 rows

T. D. Noe, Table of 50 rows

Amitabha Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 5.

Wikipedia, Difference of two squares

(Mma) ns = {3, 15, 45, 96, 192, 240, 576, 480, 720, 960, 12288}; Table[sol = Solve[x^2 - y^2 == ns[[n]] && x > 0 && y > 0, {x, y}, Integers]; Table[sol[[i, 2, 2]], {i, n}], {n, Length[ns]}]

nonn,tabl

T. D. Noe, Feb 26 2018