A299706 Number of Pythagorean triples with perimeter <= 10^n.

0, 17, 325, 4858, 64741, 808950, 9706567, 113236940, 1294080089, 14557915466

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Pythagorean Triple

Wikipedia, Tree of primitive Pythagorean triples

Example

n = 2
perimeter | Pythagorean triple
-------------------------------
   12     | [ 3,  4,  5]
   30     | [ 5, 12, 13]
   24     | [ 6,  8, 10]
   56     | [ 7, 24, 25]
   40     | [ 8, 15, 17]
   36     | [ 9, 12, 15]
   90     | [ 9, 40, 41]
   60     | [10, 24, 26]
   48     | [12, 16, 20]
   84     | [12, 35, 37]
   60     | [15, 20, 25]
   90     | [15, 36, 39]
   80     | [16, 30, 34]
   72     | [18, 24, 30]
   70     | [20, 21, 29]
   84     | [21, 28, 35]
   96     | [24, 32, 40]

Prog

(Ruby)
def f(a, b, c, n)
  return 0 if a + b + c > n
  s = n / (a + b + c)
  s += f( a - 2 * b + 2 * c,  2 * a - b + 2 * c,  2 * a - 2 * b + 3 * c, n)
  s += f( a + 2 * b + 2 * c,  2 * a + b + 2 * c,  2 * a + 2 * b + 3 * c, n)
  s += f(-a + 2 * b + 2 * c, -2 * a + b + 2 * c, -2 * a + 2 * b + 3 * c, n)
  return s
end
def A299706(n)
  (1..n).map{|i| f(3, 4, 5, 10 ** i)}
end
p A299706(8)

Crossrefs

Cf. A024155, A101929, A101930, A101931, A249750.

Sequence in context: A015693 A029535 A099275 * A318597 A142933 A180676

Adjacent sequences: A299703 A299704 A299705 * A299707 A299708 A299709

Keyword

nonn,more

Author

Seiichi Manyama, Feb 26 2018

Status

approved