Numbers x such that there is a primitive triangle whose sides are x, x-1, and 7.
4, 25, 340, 4729, 65860, 917305, 12776404, 177952345, 2478556420, 34521837529, 480827168980, 6697058528185, 93277992225604, 1299194832630265, 18095449664598100, 252037100471743129, 3510423956939805700, 48893898296685536665, 681004152196657707604
1
The sequence of primitive triangles are given in S000996. Note that the first triangle has zero area.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
Formula: s(n) = 15*s(n-1) - 15*s(n-2) + s(n-3), with initial terms 5, 17, 125.
(Mma) triArea[a_Integer, b_Integer, c_Integer] := Sqrt[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)]/4; s7 = {}; n = 0; While[Length[s7] < 7, n++; If[IntegerQ[triArea[n, n - 1, 7]], AppendTo[s7, n]]]; r7 = FindLinearRecurrence[s7]; t7 = LinearRecurrence[r7, Take[s7, Length[r7]], 30]
nonn
T. D. Noe, Apr 24 2017