S001008


Numbers x such that there is a primitive triangle whose sides are x, x-2, and 4.

3, 5, 15, 53, 195, 725, 2703, 10085, 37635, 140453, 524175, 1956245, 7300803, 27246965, 101687055, 379501253, 1416317955, 5285770565, 19726764303, 73621286645, 274758382275, 1025412242453, 3826890587535, 14282150107685, 53301709843203, 198924689265125

1

S001008

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) = 5*s(n-1) - 5*s(n-2) + s(n-3), with initial terms 3, 5, 15.

(Mma) triArea[a_Integer, b_Integer, c_Integer] := Sqrt[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)]/4; s4 = Select[Range[1000000], IntegerQ[triArea[#1, #1 - 2, 4]] &]; r4 = FindLinearRecurrence[s4]; t4 = LinearRecurrence[r4, Take[s4, Length[r4]], 30]

Cf. S000996, S001007-S001014.

nonn

T. D. Noe, Apr 24 2017

© Tony D Noe 2014-2017